(-2x)(x+3)+(3x)(x-2)=-27

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Solution for (-2x)(x+3)+(3x)(x-2)=-27 equation: 


Simplifying
(-2x)(x + 3) + (3x)(x + -2) = -27

Remove parenthesis around (-2x)
-2x(x + 3) + (3x)(x + -2) = -27

Reorder the terms:
-2x(3 + x) + (3x)(x + -2) = -27
(3 * -2x + x * -2x) + (3x)(x + -2) = -27
(-6x + -2x2) + (3x)(x + -2) = -27

Remove parenthesis around (3x)
-6x + -2x2 + 3x(x + -2) = -27

Reorder the terms:
-6x + -2x2 + 3x(-2 + x) = -27
-6x + -2x2 + (-2 * 3x + x * 3x) = -27
-6x + -2x2 + (-6x + 3x2) = -27

Reorder the terms:
-6x + -6x + -2x2 + 3x2 = -27

Combine like terms: -6x + -6x = -12x
-12x + -2x2 + 3x2 = -27

Combine like terms: -2x2 + 3x2 = 1x2
-12x + 1x2 = -27

Solving
-12x + 1x2 = -27

Solving for variable 'x'.

Reorder the terms:
27 + -12x + 1x2 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + -12x + 1x2 = 0

Factor a trinomial.
(3 + -1x)(9 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {3, 9}

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