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

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


Simplifying
9x2 + -1 = (3x + 1)(4x + 1)

Reorder the terms:
-1 + 9x2 = (3x + 1)(4x + 1)

Reorder the terms:
-1 + 9x2 = (1 + 3x)(4x + 1)

Reorder the terms:
-1 + 9x2 = (1 + 3x)(1 + 4x)

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

Combine like terms: 4x + 3x = 7x
-1 + 9x2 = (1 + 7x + 12x2)

Solving
-1 + 9x2 = 1 + 7x + 12x2

Solving for variable 'x'.

Reorder the terms:
-1 + -1 + -7x + 9x2 + -12x2 = 1 + 7x + 12x2 + -1 + -7x + -12x2

Combine like terms: -1 + -1 = -2
-2 + -7x + 9x2 + -12x2 = 1 + 7x + 12x2 + -1 + -7x + -12x2

Combine like terms: 9x2 + -12x2 = -3x2
-2 + -7x + -3x2 = 1 + 7x + 12x2 + -1 + -7x + -12x2

Reorder the terms:
-2 + -7x + -3x2 = 1 + -1 + 7x + -7x + 12x2 + -12x2

Combine like terms: 1 + -1 = 0
-2 + -7x + -3x2 = 0 + 7x + -7x + 12x2 + -12x2
-2 + -7x + -3x2 = 7x + -7x + 12x2 + -12x2

Combine like terms: 7x + -7x = 0
-2 + -7x + -3x2 = 0 + 12x2 + -12x2
-2 + -7x + -3x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
-2 + -7x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(2 + 7x + 3x2) = 0

Factor a trinomial.
-1((2 + x)(1 + 3x)) = 0

Ignore the factor -1.

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

Simplifying
2 + x = 0

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

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

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

Simplifying
x = -2

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

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {-2, -0.3333333333}

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