2x(4x+15)=27

Divide each term in 2x(4x+15)=27 by 2.

2x(4x+15)2=272

Simplify 2x(4x+15)2.

Simplify terms.

Cancel the common factor of 2.

Cancel the common factor.

2x(4x+15)2=272

Divide x(4x+15) by 1.

x(4x+15)=272

x(4x+15)=272

Apply the distributive property.

x(4x)+x⋅15=272

Reorder.

Rewrite using the commutative property of multiplication.

4x⋅x+x⋅15=272

Move 15 to the left of x.

4x⋅x+15⋅x=272

4x⋅x+15⋅x=272

4x⋅x+15⋅x=272

Multiply x by x by adding the exponents.

Move x.

4(x⋅x)+15⋅x=272

Multiply x by x.

4×2+15⋅x=272

4×2+15x=272

4×2+15x=272

4×2+15x=272

Move 272 to the left side of the equation by subtracting it from both sides.

4×2+15x-272=0

Apply the distributive property.

2(4×2)+2(15x)+2(-272)=0

Simplify.

Multiply 4 by 2.

8×2+2(15x)+2(-272)=0

Multiply 15 by 2.

8×2+30x+2(-272)=0

Cancel the common factor of 2.

Move the leading negative in -272 into the numerator.

8×2+30x+2(-272)=0

Cancel the common factor.

8×2+30x+2(-272)=0

Rewrite the expression.

8×2+30x-27=0

8×2+30x-27=0

8×2+30x-27=0

8×2+30x-27=0

Use the quadratic formula to find the solutions.

-b±b2-4(ac)2a

Substitute the values a=8, b=30, and c=-27 into the quadratic formula and solve for x.

-30±302-4⋅(8⋅-27)2⋅8

Simplify the numerator.

Raise 30 to the power of 2.

x=-30±900-4⋅(8⋅-27)2⋅8

Multiply 8 by -27.

x=-30±900-4⋅-2162⋅8

Multiply -4 by -216.

x=-30±900+8642⋅8

Add 900 and 864.

x=-30±17642⋅8

Rewrite 1764 as 422.

x=-30±4222⋅8

Pull terms out from under the radical, assuming positive real numbers.

x=-30±422⋅8

x=-30±422⋅8

Multiply 2 by 8.

x=-30±4216

Simplify -30±4216.

x=-15±218

x=-15±218

Simplify the numerator.

Raise 30 to the power of 2.

x=-30±900-4⋅(8⋅-27)2⋅8

Multiply 8 by -27.

x=-30±900-4⋅-2162⋅8

Multiply -4 by -216.

x=-30±900+8642⋅8

Add 900 and 864.

x=-30±17642⋅8

Rewrite 1764 as 422.

x=-30±4222⋅8

Pull terms out from under the radical, assuming positive real numbers.

x=-30±422⋅8

x=-30±422⋅8

Multiply 2 by 8.

x=-30±4216

Simplify -30±4216.

x=-15±218

Change the ± to +.

x=-15+218

Add -15 and 21.

x=68

Cancel the common factor of 6 and 8.

Factor 2 out of 6.

x=2(3)8

Cancel the common factors.

Factor 2 out of 8.

x=2⋅32⋅4

Cancel the common factor.

x=2⋅32⋅4

Rewrite the expression.

x=34

x=34

x=34

x=34

Simplify the numerator.

Raise 30 to the power of 2.

x=-30±900-4⋅(8⋅-27)2⋅8

Multiply 8 by -27.

x=-30±900-4⋅-2162⋅8

Multiply -4 by -216.

x=-30±900+8642⋅8

Add 900 and 864.

x=-30±17642⋅8

Rewrite 1764 as 422.

x=-30±4222⋅8

Pull terms out from under the radical, assuming positive real numbers.

x=-30±422⋅8

x=-30±422⋅8

Multiply 2 by 8.

x=-30±4216

Simplify -30±4216.

x=-15±218

Change the ± to -.

x=-15-218

Subtract 21 from -15.

x=-368

Cancel the common factor of -36 and 8.

Factor 4 out of -36.

x=4(-9)8

Cancel the common factors.

Factor 4 out of 8.

x=4⋅-94⋅2

Cancel the common factor.

x=4⋅-94⋅2

Rewrite the expression.

x=-92

x=-92

x=-92

Move the negative in front of the fraction.

x=-92

x=-92

The final answer is the combination of both solutions.

x=34,-92

Solve Using the Square Root Property 2x(4x+15)=27