(-3x-6)(-8x+9)+6x+12=0

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Solution for (-3x-6)(-8x+9)+6x+12=0 equation: 


Simplifying
(-3x + -6)(-8x + 9) + 6x + 12 = 0

Reorder the terms:
(-6 + -3x)(-8x + 9) + 6x + 12 = 0

Reorder the terms:
(-6 + -3x)(9 + -8x) + 6x + 12 = 0

Multiply (-6 + -3x) * (9 + -8x)
(-6(9 + -8x) + -3x * (9 + -8x)) + 6x + 12 = 0
((9 * -6 + -8x * -6) + -3x * (9 + -8x)) + 6x + 12 = 0
((-54 + 48x) + -3x * (9 + -8x)) + 6x + 12 = 0
(-54 + 48x + (9 * -3x + -8x * -3x)) + 6x + 12 = 0
(-54 + 48x + (-27x + 24x2)) + 6x + 12 = 0

Combine like terms: 48x + -27x = 21x
(-54 + 21x + 24x2) + 6x + 12 = 0

Reorder the terms:
-54 + 12 + 21x + 6x + 24x2 = 0

Combine like terms: -54 + 12 = -42
-42 + 21x + 6x + 24x2 = 0

Combine like terms: 21x + 6x = 27x
-42 + 27x + 24x2 = 0

Solving
-42 + 27x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 9x + 8x2) = 0

Factor a trinomial.
3((-2 + -1x)(7 + -8x)) = 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 '(7 + -8x)' equal to zero and attempt to solve:

Simplifying
7 + -8x = 0

Solving
7 + -8x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -8x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -8x = 0 + -7
-8x = 0 + -7

Combine like terms: 0 + -7 = -7
-8x = -7

Divide each side by '-8'.
x = 0.875

Simplifying
x = 0.875
Solution
x = {-2, 0.875}

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