2x(3-2x)+1=6×2-4x+1

Apply the distributive property.

2x⋅3+2x(-2x)+1=6×2-4x+1

Multiply 3 by 2.

6x+2x(-2x)+1=6×2-4x+1

Multiply x by x.

6x+2⋅-2×2+1=6×2-4x+1

Multiply 2 by -2.

6x-4×2+1=6×2-4x+1

6x-4×2+1=6×2-4x+1

Subtract 6×2 from both sides of the equation.

6x-4×2+1-6×2=-4x+1

Add 4x to both sides of the equation.

6x-4×2+1-6×2+4x=1

Add 6x and 4x.

-4×2+1-6×2+10x=1

Subtract 6×2 from -4×2.

-10×2+1+10x=1

-10×2+1+10x=1

Move 1 to the left side of the equation by subtracting it from both sides.

-10×2+1+10x-1=0

Subtract 1 from 1.

-10×2+10x+0=0

Add -10×2+10x and 0.

-10×2+10x=0

-10×2+10x=0

Factor -10x out of -10×2.

-10x⋅x+10x=0

Factor -10x out of 10x.

-10x⋅x-10x⋅-1=0

Factor -10x out of -10x(x)-10x(-1).

-10x(x-1)=0

-10x(x-1)=0

Divide each term in -10x(x-1)=0 by -10.

-10x(x-1)-10=0-10

Simplify -10x(x-1)-10.

Simplify terms.

Cancel the common factor of -10.

Cancel the common factor.

-10x(x-1)-10=0-10

Divide x(x-1) by 1.

x(x-1)=0-10

x(x-1)=0-10

Apply the distributive property.

x⋅x+x⋅-1=0-10

Simplify the expression.

Multiply x by x.

x2+x⋅-1=0-10

Move -1 to the left of x.

x2-1⋅x=0-10

x2-1⋅x=0-10

x2-1⋅x=0-10

Rewrite -1x as -x.

x2-x=0-10

x2-x=0-10

Divide 0 by -10.

x2-x=0

x2-x=0

Factor x out of x2.

x⋅x-x=0

Factor x out of -x.

x⋅x+x⋅-1=0

Factor x out of x⋅x+x⋅-1.

x(x-1)=0

x(x-1)=0

If any individual factor on the left side of the equation is equal to 0, the entire expression will be equal to 0.

x=0

x-1=0

Set the first factor equal to 0.

x=0

Set the next factor equal to 0.

x-1=0

Add 1 to both sides of the equation.

x=1

x=1

The final solution is all the values that make x(x-1)=0 true.

x=0,1

Solve Using the Square Root Property 2x(3-2x)+1=6x^2-4x+1