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

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


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

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

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

Multiply (2 + 9x) * (-1 + 9x)
(2(-1 + 9x) + 9x * (-1 + 9x)) = 9x2 + 3x + -2
((-1 * 2 + 9x * 2) + 9x * (-1 + 9x)) = 9x2 + 3x + -2
((-2 + 18x) + 9x * (-1 + 9x)) = 9x2 + 3x + -2
(-2 + 18x + (-1 * 9x + 9x * 9x)) = 9x2 + 3x + -2
(-2 + 18x + (-9x + 81x2)) = 9x2 + 3x + -2

Combine like terms: 18x + -9x = 9x
(-2 + 9x + 81x2) = 9x2 + 3x + -2

Reorder the terms:
-2 + 9x + 81x2 = -2 + 3x + 9x2

Add '2' to each side of the equation.
-2 + 9x + 2 + 81x2 = -2 + 3x + 2 + 9x2

Reorder the terms:
-2 + 2 + 9x + 81x2 = -2 + 3x + 2 + 9x2

Combine like terms: -2 + 2 = 0
0 + 9x + 81x2 = -2 + 3x + 2 + 9x2
9x + 81x2 = -2 + 3x + 2 + 9x2

Reorder the terms:
9x + 81x2 = -2 + 2 + 3x + 9x2

Combine like terms: -2 + 2 = 0
9x + 81x2 = 0 + 3x + 9x2
9x + 81x2 = 3x + 9x2

Solving
9x + 81x2 = 3x + 9x2

Solving for variable 'x'.

Reorder the terms:
9x + -3x + 81x2 + -9x2 = 3x + 9x2 + -3x + -9x2

Combine like terms: 9x + -3x = 6x
6x + 81x2 + -9x2 = 3x + 9x2 + -3x + -9x2

Combine like terms: 81x2 + -9x2 = 72x2
6x + 72x2 = 3x + 9x2 + -3x + -9x2

Reorder the terms:
6x + 72x2 = 3x + -3x + 9x2 + -9x2

Combine like terms: 3x + -3x = 0
6x + 72x2 = 0 + 9x2 + -9x2
6x + 72x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
6x + 72x2 = 0

Factor out the Greatest Common Factor (GCF), '6x'.
6x(1 + 12x) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(1 + 12x)' equal to zero and attempt to solve:

Simplifying
1 + 12x = 0

Solving
1 + 12x = 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 + 12x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 12x = 0 + -1
12x = 0 + -1

Combine like terms: 0 + -1 = -1
12x = -1

Divide each side by '12'.
x = -0.08333333333

Simplifying
x = -0.08333333333
Solution
x = {0, -0.08333333333}

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