(x-6)(x+2)-9=-3(x+3)

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Solution for (x-6)(x+2)-9=-3(x+3) equation: 


Simplifying
(x + -6)(x + 2) + -9 = -3(x + 3)

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

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

Multiply (-6 + x) * (2 + x)
(-6(2 + x) + x(2 + x)) + -9 = -3(x + 3)
((2 * -6 + x * -6) + x(2 + x)) + -9 = -3(x + 3)
((-12 + -6x) + x(2 + x)) + -9 = -3(x + 3)
(-12 + -6x + (2 * x + x * x)) + -9 = -3(x + 3)
(-12 + -6x + (2x + x2)) + -9 = -3(x + 3)

Combine like terms: -6x + 2x = -4x
(-12 + -4x + x2) + -9 = -3(x + 3)

Reorder the terms:
-12 + -9 + -4x + x2 = -3(x + 3)

Combine like terms: -12 + -9 = -21
-21 + -4x + x2 = -3(x + 3)

Reorder the terms:
-21 + -4x + x2 = -3(3 + x)
-21 + -4x + x2 = (3 * -3 + x * -3)
-21 + -4x + x2 = (-9 + -3x)

Solving
-21 + -4x + x2 = -9 + -3x

Solving for variable 'x'.

Reorder the terms:
-21 + 9 + -4x + 3x + x2 = -9 + -3x + 9 + 3x

Combine like terms: -21 + 9 = -12
-12 + -4x + 3x + x2 = -9 + -3x + 9 + 3x

Combine like terms: -4x + 3x = -1x
-12 + -1x + x2 = -9 + -3x + 9 + 3x

Reorder the terms:
-12 + -1x + x2 = -9 + 9 + -3x + 3x

Combine like terms: -9 + 9 = 0
-12 + -1x + x2 = 0 + -3x + 3x
-12 + -1x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-12 + -1x + x2 = 0

Factor a trinomial.
(-3 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-3, 4}

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