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

2x(3-2x)+1=6×2-4x+1
Simplify each term.
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
Move all terms containing x to the left side of the equation.
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
-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
Combine the opposite terms in -10×2+1+10x-1.
Subtract 1 from 1.
-10×2+10x+0=0
-10×2+10x=0
-10×2+10x=0
Factor -10x out of -10×2+10x.
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 by -10 and simplify.
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.
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 and solve.
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