9x^2-4+(x+1)(3x+2)+(12x+8)(3x-2)=0

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Solution for 9x^2-4+(x+1)(3x+2)+(12x+8)(3x-2)=0 equation: 


Simplifying
9x2 + -4 + (x + 1)(3x + 2) + (12x + 8)(3x + -2) = 0

Reorder the terms:
9x2 + -4 + (1 + x)(3x + 2) + (12x + 8)(3x + -2) = 0

Reorder the terms:
9x2 + -4 + (1 + x)(2 + 3x) + (12x + 8)(3x + -2) = 0

Multiply (1 + x) * (2 + 3x)
9x2 + -4 + (1(2 + 3x) + x(2 + 3x)) + (12x + 8)(3x + -2) = 0
9x2 + -4 + ((2 * 1 + 3x * 1) + x(2 + 3x)) + (12x + 8)(3x + -2) = 0
9x2 + -4 + ((2 + 3x) + x(2 + 3x)) + (12x + 8)(3x + -2) = 0
9x2 + -4 + (2 + 3x + (2 * x + 3x * x)) + (12x + 8)(3x + -2) = 0
9x2 + -4 + (2 + 3x + (2x + 3x2)) + (12x + 8)(3x + -2) = 0

Combine like terms: 3x + 2x = 5x
9x2 + -4 + (2 + 5x + 3x2) + (12x + 8)(3x + -2) = 0

Reorder the terms:
9x2 + -4 + 2 + 5x + 3x2 + (8 + 12x)(3x + -2) = 0

Reorder the terms:
9x2 + -4 + 2 + 5x + 3x2 + (8 + 12x)(-2 + 3x) = 0

Multiply (8 + 12x) * (-2 + 3x)
9x2 + -4 + 2 + 5x + 3x2 + (8(-2 + 3x) + 12x * (-2 + 3x)) = 0
9x2 + -4 + 2 + 5x + 3x2 + ((-2 * 8 + 3x * 8) + 12x * (-2 + 3x)) = 0
9x2 + -4 + 2 + 5x + 3x2 + ((-16 + 24x) + 12x * (-2 + 3x)) = 0
9x2 + -4 + 2 + 5x + 3x2 + (-16 + 24x + (-2 * 12x + 3x * 12x)) = 0
9x2 + -4 + 2 + 5x + 3x2 + (-16 + 24x + (-24x + 36x2)) = 0

Combine like terms: 24x + -24x = 0
9x2 + -4 + 2 + 5x + 3x2 + (-16 + 0 + 36x2) = 0
9x2 + -4 + 2 + 5x + 3x2 + (-16 + 36x2) = 0

Reorder the terms:
-4 + 2 + -16 + 5x + 9x2 + 3x2 + 36x2 = 0

Combine like terms: -4 + 2 = -2
-2 + -16 + 5x + 9x2 + 3x2 + 36x2 = 0

Combine like terms: -2 + -16 = -18
-18 + 5x + 9x2 + 3x2 + 36x2 = 0

Combine like terms: 9x2 + 3x2 = 12x2
-18 + 5x + 12x2 + 36x2 = 0

Combine like terms: 12x2 + 36x2 = 48x2
-18 + 5x + 48x2 = 0

Solving
-18 + 5x + 48x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -3x)(9 + -16x) = 0


Subproblem 1
Set the factor '(-2 + -3x)' equal to zero and attempt to solve:

Simplifying
-2 + -3x = 0

Solving
-2 + -3x = 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 + -3x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3x = 0 + 2
-3x = 0 + 2

Combine like terms: 0 + 2 = 2
-3x = 2

Divide each side by '-3'.
x = -0.6666666667

Simplifying
x = -0.6666666667

Subproblem 2
Set the factor '(9 + -16x)' equal to zero and attempt to solve:

Simplifying
9 + -16x = 0

Solving
9 + -16x = 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 + -16x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -16x = 0 + -9
-16x = 0 + -9

Combine like terms: 0 + -9 = -9
-16x = -9

Divide each side by '-16'.
x = 0.5625

Simplifying
x = 0.5625
Solution
x = {-0.6666666667, 0.5625}

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