(x^2-3x)(-2x-6)=0

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Solution for (x^2-3x)(-2x-6)=0 equation: 


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

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

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

Multiply (-3x + x2) * (-6 + -2x)
(-3x * (-6 + -2x) + x2(-6 + -2x)) = 0
((-6 * -3x + -2x * -3x) + x2(-6 + -2x)) = 0
((18x + 6x2) + x2(-6 + -2x)) = 0
(18x + 6x2 + (-6 * x2 + -2x * x2)) = 0
(18x + 6x2 + (-6x2 + -2x3)) = 0

Combine like terms: 6x2 + -6x2 = 0
(18x + 0 + -2x3) = 0
(18x + -2x3) = 0

Solving
18x + -2x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(9 + -1x2) = 0

Factor a difference between two squares.
2x((3 + x)(3 + -1x)) = 0

Ignore the factor 2.

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 '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3

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

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, -3, 3}

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