2(3x-9)=-3x(x-3)

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Solution for 2(3x-9)=-3x(x-3) equation: 


Simplifying
2(3x + -9) = -3x(x + -3)

Reorder the terms:
2(-9 + 3x) = -3x(x + -3)
(-9 * 2 + 3x * 2) = -3x(x + -3)
(-18 + 6x) = -3x(x + -3)

Reorder the terms:
-18 + 6x = -3x(-3 + x)
-18 + 6x = (-3 * -3x + x * -3x)
-18 + 6x = (9x + -3x2)

Solving
-18 + 6x = 9x + -3x2

Solving for variable 'x'.

Combine like terms: 6x + -9x = -3x
-18 + -3x + 3x2 = 9x + -3x2 + -9x + 3x2

Reorder the terms:
-18 + -3x + 3x2 = 9x + -9x + -3x2 + 3x2

Combine like terms: 9x + -9x = 0
-18 + -3x + 3x2 = 0 + -3x2 + 3x2
-18 + -3x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
-18 + -3x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -1x + x2) = 0

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

Ignore the factor 3.

Subproblem 1
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

Subproblem 2
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 = {-2, 3}

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