12x^2-(3x-4)(3x+4)=6x+40

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Solution for 12x^2-(3x-4)(3x+4)=6x+40 equation: 


Simplifying
12x2 + -1(3x + -4)(3x + 4) = 6x + 40

Reorder the terms:
12x2 + -1(-4 + 3x)(3x + 4) = 6x + 40

Reorder the terms:
12x2 + -1(-4 + 3x)(4 + 3x) = 6x + 40

Multiply (-4 + 3x) * (4 + 3x)
12x2 + -1(-4(4 + 3x) + 3x * (4 + 3x)) = 6x + 40
12x2 + -1((4 * -4 + 3x * -4) + 3x * (4 + 3x)) = 6x + 40
12x2 + -1((-16 + -12x) + 3x * (4 + 3x)) = 6x + 40
12x2 + -1(-16 + -12x + (4 * 3x + 3x * 3x)) = 6x + 40
12x2 + -1(-16 + -12x + (12x + 9x2)) = 6x + 40

Combine like terms: -12x + 12x = 0
12x2 + -1(-16 + 0 + 9x2) = 6x + 40
12x2 + -1(-16 + 9x2) = 6x + 40
12x2 + (-16 * -1 + 9x2 * -1) = 6x + 40
12x2 + (16 + -9x2) = 6x + 40

Reorder the terms:
16 + 12x2 + -9x2 = 6x + 40

Combine like terms: 12x2 + -9x2 = 3x2
16 + 3x2 = 6x + 40

Reorder the terms:
16 + 3x2 = 40 + 6x

Solving
16 + 3x2 = 40 + 6x

Solving for variable 'x'.

Reorder the terms:
16 + -40 + -6x + 3x2 = 40 + 6x + -40 + -6x

Combine like terms: 16 + -40 = -24
-24 + -6x + 3x2 = 40 + 6x + -40 + -6x

Reorder the terms:
-24 + -6x + 3x2 = 40 + -40 + 6x + -6x

Combine like terms: 40 + -40 = 0
-24 + -6x + 3x2 = 0 + 6x + -6x
-24 + -6x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-24 + -6x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -2x + x2) = 0

Factor a trinomial.
3((-2 + -1x)(4 + -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 '(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 = {-2, 4}

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