(3x-2)(3x-2)+(2x)(2x)=(3x+2)(3x+2)

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


Simplifying
(3x + -2)(3x + -2) + (2x)(2x) = (3x + 2)(3x + 2)

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

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

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

Combine like terms: -6x + -6x = -12x
(4 + -12x + 9x2) + (2x)(2x) = (3x + 2)(3x + 2)

Remove parenthesis around (2x)
4 + -12x + 9x2 + 2x(2x) = (3x + 2)(3x + 2)

Remove parenthesis around (2x)
4 + -12x + 9x2 + 2x * 2x = (3x + 2)(3x + 2)

Reorder the terms for easier multiplication:
4 + -12x + 9x2 + 2 * 2x * x = (3x + 2)(3x + 2)

Multiply 2 * 2
4 + -12x + 9x2 + 4x * x = (3x + 2)(3x + 2)

Multiply x * x
4 + -12x + 9x2 + 4x2 = (3x + 2)(3x + 2)

Combine like terms: 9x2 + 4x2 = 13x2
4 + -12x + 13x2 = (3x + 2)(3x + 2)

Reorder the terms:
4 + -12x + 13x2 = (2 + 3x)(3x + 2)

Reorder the terms:
4 + -12x + 13x2 = (2 + 3x)(2 + 3x)

Multiply (2 + 3x) * (2 + 3x)
4 + -12x + 13x2 = (2(2 + 3x) + 3x * (2 + 3x))
4 + -12x + 13x2 = ((2 * 2 + 3x * 2) + 3x * (2 + 3x))
4 + -12x + 13x2 = ((4 + 6x) + 3x * (2 + 3x))
4 + -12x + 13x2 = (4 + 6x + (2 * 3x + 3x * 3x))
4 + -12x + 13x2 = (4 + 6x + (6x + 9x2))

Combine like terms: 6x + 6x = 12x
4 + -12x + 13x2 = (4 + 12x + 9x2)

Add '-4' to each side of the equation.
4 + -12x + -4 + 13x2 = 4 + 12x + -4 + 9x2

Reorder the terms:
4 + -4 + -12x + 13x2 = 4 + 12x + -4 + 9x2

Combine like terms: 4 + -4 = 0
0 + -12x + 13x2 = 4 + 12x + -4 + 9x2
-12x + 13x2 = 4 + 12x + -4 + 9x2

Reorder the terms:
-12x + 13x2 = 4 + -4 + 12x + 9x2

Combine like terms: 4 + -4 = 0
-12x + 13x2 = 0 + 12x + 9x2
-12x + 13x2 = 12x + 9x2

Solving
-12x + 13x2 = 12x + 9x2

Solving for variable 'x'.

Reorder the terms:
-12x + -12x + 13x2 + -9x2 = 12x + 9x2 + -12x + -9x2

Combine like terms: -12x + -12x = -24x
-24x + 13x2 + -9x2 = 12x + 9x2 + -12x + -9x2

Combine like terms: 13x2 + -9x2 = 4x2
-24x + 4x2 = 12x + 9x2 + -12x + -9x2

Reorder the terms:
-24x + 4x2 = 12x + -12x + 9x2 + -9x2

Combine like terms: 12x + -12x = 0
-24x + 4x2 = 0 + 9x2 + -9x2
-24x + 4x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(-6 + x) = 0

Ignore the factor 4.

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 '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 x = 6 Simplifying x = 6

Solution

x = {0, 6}

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