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

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


Simplifying
9x2 + -1 = (3x + -1)(x + 2)

Reorder the terms:
-1 + 9x2 = (3x + -1)(x + 2)

Reorder the terms:
-1 + 9x2 = (-1 + 3x)(x + 2)

Reorder the terms:
-1 + 9x2 = (-1 + 3x)(2 + x)

Multiply (-1 + 3x) * (2 + x)
-1 + 9x2 = (-1(2 + x) + 3x * (2 + x))
-1 + 9x2 = ((2 * -1 + x * -1) + 3x * (2 + x))
-1 + 9x2 = ((-2 + -1x) + 3x * (2 + x))
-1 + 9x2 = (-2 + -1x + (2 * 3x + x * 3x))
-1 + 9x2 = (-2 + -1x + (6x + 3x2))

Combine like terms: -1x + 6x = 5x
-1 + 9x2 = (-2 + 5x + 3x2)

Solving
-1 + 9x2 = -2 + 5x + 3x2

Solving for variable 'x'.

Reorder the terms:
-1 + 2 + -5x + 9x2 + -3x2 = -2 + 5x + 3x2 + 2 + -5x + -3x2

Combine like terms: -1 + 2 = 1
1 + -5x + 9x2 + -3x2 = -2 + 5x + 3x2 + 2 + -5x + -3x2

Combine like terms: 9x2 + -3x2 = 6x2
1 + -5x + 6x2 = -2 + 5x + 3x2 + 2 + -5x + -3x2

Reorder the terms:
1 + -5x + 6x2 = -2 + 2 + 5x + -5x + 3x2 + -3x2

Combine like terms: -2 + 2 = 0
1 + -5x + 6x2 = 0 + 5x + -5x + 3x2 + -3x2
1 + -5x + 6x2 = 5x + -5x + 3x2 + -3x2

Combine like terms: 5x + -5x = 0
1 + -5x + 6x2 = 0 + 3x2 + -3x2
1 + -5x + 6x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
1 + -5x + 6x2 = 0

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


Subproblem 1
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

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {0.3333333333, 0.5}

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