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

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


Simplifying
x2 + -1 + (3x + -3)(4x + 3) = 0

Reorder the terms:
x2 + -1 + (-3 + 3x)(4x + 3) = 0

Reorder the terms:
x2 + -1 + (-3 + 3x)(3 + 4x) = 0

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

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

Reorder the terms:
-1 + -9 + -3x + x2 + 12x2 = 0

Combine like terms: -1 + -9 = -10
-10 + -3x + x2 + 12x2 = 0

Combine like terms: x2 + 12x2 = 13x2
-10 + -3x + 13x2 = 0

Solving
-10 + -3x + 13x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-10 + -13x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-10 + -13x)' equal to zero and attempt to solve:

Simplifying
-10 + -13x = 0

Solving
-10 + -13x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -13x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -13x = 0 + 10
-13x = 0 + 10

Combine like terms: 0 + 10 = 10
-13x = 10

Divide each side by '-13'.
x = -0.7692307692

Simplifying
x = -0.7692307692

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-0.7692307692, 1}

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