# Solve Using the Square Root Property -3x^2+7x=6x^2-5x -3×2+7x=6×2-5x
Move all terms containing x to the left side of the equation.
Subtract 6×2 from both sides of the equation.
-3×2+7x-6×2=-5x
Add 5x to both sides of the equation.
-3×2+7x-6×2+5x=0
Subtract 6×2 from -3×2.
-9×2+7x+5x=0
-9×2+12x=0
-9×2+12x=0
Factor -3x out of -9×2+12x.
Factor -3x out of -9×2.
-3x(3x)+12x=0
Factor -3x out of 12x.
-3x(3x)-3x⋅-4=0
Factor -3x out of -3x(3x)-3x(-4).
-3x(3x-4)=0
-3x(3x-4)=0
Divide each term by -3 and simplify.
Divide each term in -3x(3x-4)=0 by -3.
-3x(3x-4)-3=0-3
Simplify -3x(3x-4)-3.
Simplify terms.
Cancel the common factor of -3.
Cancel the common factor.
-3x(3x-4)-3=0-3
Divide x(3x-4) by 1.
x(3x-4)=0-3
x(3x-4)=0-3
Apply the distributive property.
x(3x)+x⋅-4=0-3
Reorder.
Rewrite using the commutative property of multiplication.
3x⋅x+x⋅-4=0-3
Move -4 to the left of x.
3x⋅x-4⋅x=0-3
3x⋅x-4⋅x=0-3
3x⋅x-4⋅x=0-3
Multiply x by x by adding the exponents.
Move x.
3(x⋅x)-4⋅x=0-3
Multiply x by x.
3×2-4⋅x=0-3
3×2-4x=0-3
3×2-4x=0-3
Divide 0 by -3.
3×2-4x=0
3×2-4x=0
Factor x out of 3×2-4x.
Factor x out of 3×2.
x(3x)-4x=0
Factor x out of -4x.
x(3x)+x⋅-4=0
Factor x out of x(3x)+x⋅-4.
x(3x-4)=0
x(3x-4)=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
3x-4=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.
3x-4=0
Add 4 to both sides of the equation.
3x=4
Divide each term by 3 and simplify.
Divide each term in 3x=4 by 3.
3×3=43
Cancel the common factor of 3.
Cancel the common factor.
3×3=43
Divide x by 1.
x=43
x=43
x=43
x=43
The final solution is all the values that make x(3x-4)=0 true.
x=0,43
Solve Using the Square Root Property -3x^2+7x=6x^2-5x     