(x^2-2x)(-3x+6)=

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Solution for (x^2-2x)(-3x+6)= equation:


Simplifying
(x2 + -2x)(-3x + 6) = 0

Reorder the terms:
(-2x + x2)(-3x + 6) = 0

Reorder the terms:
(-2x + x2)(6 + -3x) = 0

Multiply (-2x + x2) * (6 + -3x)
(-2x * (6 + -3x) + x2(6 + -3x)) = 0
((6 * -2x + -3x * -2x) + x2(6 + -3x)) = 0
((-12x + 6x2) + x2(6 + -3x)) = 0
(-12x + 6x2 + (6 * x2 + -3x * x2)) = 0
(-12x + 6x2 + (6x2 + -3x3)) = 0

Combine like terms: 6x2 + 6x2 = 12x2
(-12x + 12x2 + -3x3) = 0

Solving
-12x + 12x2 + -3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-4 + 4x + -1x2) = 0

Factor a trinomial.
3x((-2 + x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

Move all terms containing x to the left, all other terms to the right.

Simplifying
x = 0

Subproblem 2
Set the factor '(-2 + x)' equal to zero and attempt to solve:

Simplifying
-2 + x = 0

Solving
-2 + x = 0

Move all terms containing x to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + x = 0 + 2
x = 0 + 2

Combine like terms: 0 + 2 = 2
x = 2

Simplifying
x = 2

Subproblem 3
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 2, 2}

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