-(5z(10z+2))=2+(4z+3)

Apply the distributive property.

-(5z(10z)+5z⋅2)=2+4z+3

Simplify the expression.

Multiply z by z.

-(5⋅10z2+5z⋅2)=2+4z+3

Multiply 2 by 5.

-(5⋅10z2+10z)=2+4z+3

Multiply 5 by 10.

-(50z2+10z)=2+4z+3

-(50z2+10z)=2+4z+3

Apply the distributive property.

-(50z2)-(10z)=2+4z+3

Multiply.

Multiply 50 by -1.

-50z2-(10z)=2+4z+3

Multiply 10 by -1.

-50z2-10z=2+4z+3

-50z2-10z=2+4z+3

-50z2-10z=2+4z+3

Add 2 and 3.

-50z2-10z=4z+5

Subtract 4z from both sides of the equation.

-50z2-10z-4z=5

Subtract 4z from -10z.

-50z2-14z=5

-50z2-14z=5

Move 5 to the left side of the equation by subtracting it from both sides.

-50z2-14z-5=0

Factor -1 out of -50z2.

-(50z2)-14z-5=0

Factor -1 out of -14z.

-(50z2)-(14z)-5=0

Rewrite -5 as -1(5).

-(50z2)-(14z)-1⋅5=0

Factor -1 out of -(50z2)-(14z).

-(50z2+14z)-1⋅5=0

Factor -1 out of -(50z2+14z)-1(5).

-(50z2+14z+5)=0

-(50z2+14z+5)=0

Multiply each term in -(50z2+14z+5)=0 by -1.

-(50z2+14z+5)⋅-1=0⋅-1

Simplify -(50z2+14z+5)⋅-1.

Apply the distributive property.

(-(50z2)-(14z)-1⋅5)⋅-1=0⋅-1

Simplify.

Multiply 50 by -1.

(-50z2-(14z)-1⋅5)⋅-1=0⋅-1

Multiply 14 by -1.

(-50z2-14z-1⋅5)⋅-1=0⋅-1

Multiply -1 by 5.

(-50z2-14z-5)⋅-1=0⋅-1

(-50z2-14z-5)⋅-1=0⋅-1

Apply the distributive property.

-50z2⋅-1-14z⋅-1-5⋅-1=0⋅-1

Simplify.

Multiply -1 by -50.

50z2-14z⋅-1-5⋅-1=0⋅-1

Multiply -1 by -14.

50z2+14z-5⋅-1=0⋅-1

Multiply -5 by -1.

50z2+14z+5=0⋅-1

50z2+14z+5=0⋅-1

50z2+14z+5=0⋅-1

Multiply 0 by -1.

50z2+14z+5=0

50z2+14z+5=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=50, b=14, and c=5 into the quadratic formula and solve for z.

-14±142-4⋅(50⋅5)2⋅50

Simplify the numerator.

Raise 14 to the power of 2.

z=-14±196-4⋅(50⋅5)2⋅50

Multiply 50 by 5.

z=-14±196-4⋅2502⋅50

Multiply -4 by 250.

z=-14±196-10002⋅50

Subtract 1000 from 196.

z=-14±-8042⋅50

Rewrite -804 as -1(804).

z=-14±-1⋅8042⋅50

Rewrite -1(804) as -1⋅804.

z=-14±-1⋅8042⋅50

Rewrite -1 as i.

z=-14±i⋅8042⋅50

Rewrite 804 as 22⋅201.

Factor 4 out of 804.

z=-14±i⋅4(201)2⋅50

Rewrite 4 as 22.

z=-14±i⋅22⋅2012⋅50

z=-14±i⋅22⋅2012⋅50

Pull terms out from under the radical.

z=-14±i⋅(2201)2⋅50

Move 2 to the left of i.

z=-14±2i2012⋅50

z=-14±2i2012⋅50

Multiply 2 by 50.

z=-14±2i201100

Simplify -14±2i201100.

z=-7±i20150

z=-7±i20150

Simplify the numerator.

Raise 14 to the power of 2.

z=-14±196-4⋅(50⋅5)2⋅50

Multiply 50 by 5.

z=-14±196-4⋅2502⋅50

Multiply -4 by 250.

z=-14±196-10002⋅50

Subtract 1000 from 196.

z=-14±-8042⋅50

Rewrite -804 as -1(804).

z=-14±-1⋅8042⋅50

Rewrite -1(804) as -1⋅804.

z=-14±-1⋅8042⋅50

Rewrite -1 as i.

z=-14±i⋅8042⋅50

Rewrite 804 as 22⋅201.

Factor 4 out of 804.

z=-14±i⋅4(201)2⋅50

Rewrite 4 as 22.

z=-14±i⋅22⋅2012⋅50

z=-14±i⋅22⋅2012⋅50

Pull terms out from under the radical.

z=-14±i⋅(2201)2⋅50

Move 2 to the left of i.

z=-14±2i2012⋅50

z=-14±2i2012⋅50

Multiply 2 by 50.

z=-14±2i201100

Simplify -14±2i201100.

z=-7±i20150

Change the ± to +.

z=-7+i20150

Rewrite -7 as -1(7).

z=-1⋅7+i20150

Factor -1 out of i201.

z=-1⋅7-(-i201)50

Factor -1 out of -1(7)-(-i201).

z=-1(7-i201)50

Move the negative in front of the fraction.

z=-7-i20150

z=-7-i20150

Simplify the numerator.

Raise 14 to the power of 2.

z=-14±196-4⋅(50⋅5)2⋅50

Multiply 50 by 5.

z=-14±196-4⋅2502⋅50

Multiply -4 by 250.

z=-14±196-10002⋅50

Subtract 1000 from 196.

z=-14±-8042⋅50

Rewrite -804 as -1(804).

z=-14±-1⋅8042⋅50

Rewrite -1(804) as -1⋅804.

z=-14±-1⋅8042⋅50

Rewrite -1 as i.

z=-14±i⋅8042⋅50

Rewrite 804 as 22⋅201.

Factor 4 out of 804.

z=-14±i⋅4(201)2⋅50

Rewrite 4 as 22.

z=-14±i⋅22⋅2012⋅50

z=-14±i⋅22⋅2012⋅50

Pull terms out from under the radical.

z=-14±i⋅(2201)2⋅50

Move 2 to the left of i.

z=-14±2i2012⋅50

z=-14±2i2012⋅50

Multiply 2 by 50.

z=-14±2i201100

Simplify -14±2i201100.

z=-7±i20150

Change the ± to -.

z=-7-i20150

Rewrite -7 as -1(7).

z=-1⋅7-i20150

Factor -1 out of -i201.

z=-1⋅7-(i201)50

Factor -1 out of -1(7)-(i201).

z=-1(7+i201)50

Move the negative in front of the fraction.

z=-7+i20150

z=-7+i20150

The final answer is the combination of both solutions.

z=-7-i20150,-7+i20150

Solve using the Square Root Property -(5z(10z+2))=2+(4z+3)