(3x+4)(x-5)-9x-12=0

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Solution for (3x+4)(x-5)-9x-12=0 equation: 


Simplifying
(3x + 4)(x + -5) + -9x + -12 = 0

Reorder the terms:
(4 + 3x)(x + -5) + -9x + -12 = 0

Reorder the terms:
(4 + 3x)(-5 + x) + -9x + -12 = 0

Multiply (4 + 3x) * (-5 + x)
(4(-5 + x) + 3x * (-5 + x)) + -9x + -12 = 0
((-5 * 4 + x * 4) + 3x * (-5 + x)) + -9x + -12 = 0
((-20 + 4x) + 3x * (-5 + x)) + -9x + -12 = 0
(-20 + 4x + (-5 * 3x + x * 3x)) + -9x + -12 = 0
(-20 + 4x + (-15x + 3x2)) + -9x + -12 = 0

Combine like terms: 4x + -15x = -11x
(-20 + -11x + 3x2) + -9x + -12 = 0

Reorder the terms:
-20 + -12 + -11x + -9x + 3x2 = 0

Combine like terms: -20 + -12 = -32
-32 + -11x + -9x + 3x2 = 0

Combine like terms: -11x + -9x = -20x
-32 + -20x + 3x2 = 0

Solving
-32 + -20x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -3x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 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 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-1.333333333, 8}

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