(3x+2)(3x-2)-9(x+1)2=-22

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Solution for (3x+2)(3x-2)-9(x+1)2=-22 equation:


Simplifying
(3x + 2)(3x + -2) + -9(x + 1) * 2 = -22

Reorder the terms:
(2 + 3x)(3x + -2) + -9(x + 1) * 2 = -22

Reorder the terms:
(2 + 3x)(-2 + 3x) + -9(x + 1) * 2 = -22

Multiply (2 + 3x) * (-2 + 3x)
(2(-2 + 3x) + 3x * (-2 + 3x)) + -9(x + 1) * 2 = -22
((-2 * 2 + 3x * 2) + 3x * (-2 + 3x)) + -9(x + 1) * 2 = -22
((-4 + 6x) + 3x * (-2 + 3x)) + -9(x + 1) * 2 = -22
(-4 + 6x + (-2 * 3x + 3x * 3x)) + -9(x + 1) * 2 = -22
(-4 + 6x + (-6x + 9x2)) + -9(x + 1) * 2 = -22

Combine like terms: 6x + -6x = 0
(-4 + 0 + 9x2) + -9(x + 1) * 2 = -22
(-4 + 9x2) + -9(x + 1) * 2 = -22

Reorder the terms:
-4 + 9x2 + -9(1 + x) * 2 = -22

Reorder the terms for easier multiplication:
-4 + 9x2 + -9 * 2(1 + x) = -22

Multiply -9 * 2
-4 + 9x2 + -18(1 + x) = -22
-4 + 9x2 + (1 * -18 + x * -18) = -22
-4 + 9x2 + (-18 + -18x) = -22

Reorder the terms:
-4 + -18 + -18x + 9x2 = -22

Combine like terms: -4 + -18 = -22
-22 + -18x + 9x2 = -22

Add '22' to each side of the equation.
-22 + -18x + 22 + 9x2 = -22 + 22

Reorder the terms:
-22 + 22 + -18x + 9x2 = -22 + 22

Combine like terms: -22 + 22 = 0
0 + -18x + 9x2 = -22 + 22
-18x + 9x2 = -22 + 22

Combine like terms: -22 + 22 = 0
-18x + 9x2 = 0

Solving
-18x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '9x'.
9x(-2 + x) = 0

Ignore the factor 9.

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 '(-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
Solution
x = {0, 2}

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