(3x)(3x)=(3x+6)(3x+6)-(x+6)(x+6)

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Solution for (3x)(3x)=(3x+6)(3x+6)-(x+6)(x+6) equation:


Simplifying
(3x)(3x) = (3x + 6)(3x + 6) + -1(x + 6)(x + 6)

Remove parenthesis around (3x)
3x(3x) = (3x + 6)(3x + 6) + -1(x + 6)(x + 6)

Remove parenthesis around (3x)
3x * 3x = (3x + 6)(3x + 6) + -1(x + 6)(x + 6)

Reorder the terms for easier multiplication:
3 * 3x * x = (3x + 6)(3x + 6) + -1(x + 6)(x + 6)

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

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

Reorder the terms:
9x2 = (6 + 3x)(3x + 6) + -1(x + 6)(x + 6)

Reorder the terms:
9x2 = (6 + 3x)(6 + 3x) + -1(x + 6)(x + 6)

Multiply (6 + 3x) * (6 + 3x)
9x2 = (6(6 + 3x) + 3x * (6 + 3x)) + -1(x + 6)(x + 6)
9x2 = ((6 * 6 + 3x * 6) + 3x * (6 + 3x)) + -1(x + 6)(x + 6)
9x2 = ((36 + 18x) + 3x * (6 + 3x)) + -1(x + 6)(x + 6)
9x2 = (36 + 18x + (6 * 3x + 3x * 3x)) + -1(x + 6)(x + 6)
9x2 = (36 + 18x + (18x + 9x2)) + -1(x + 6)(x + 6)

Combine like terms: 18x + 18x = 36x
9x2 = (36 + 36x + 9x2) + -1(x + 6)(x + 6)

Reorder the terms:
9x2 = 36 + 36x + 9x2 + -1(6 + x)(x + 6)

Reorder the terms:
9x2 = 36 + 36x + 9x2 + -1(6 + x)(6 + x)

Multiply (6 + x) * (6 + x)
9x2 = 36 + 36x + 9x2 + -1(6(6 + x) + x(6 + x))
9x2 = 36 + 36x + 9x2 + -1((6 * 6 + x * 6) + x(6 + x))
9x2 = 36 + 36x + 9x2 + -1((36 + 6x) + x(6 + x))
9x2 = 36 + 36x + 9x2 + -1(36 + 6x + (6 * x + x * x))
9x2 = 36 + 36x + 9x2 + -1(36 + 6x + (6x + x2))

Combine like terms: 6x + 6x = 12x
9x2 = 36 + 36x + 9x2 + -1(36 + 12x + x2)
9x2 = 36 + 36x + 9x2 + (36 * -1 + 12x * -1 + x2 * -1)
9x2 = 36 + 36x + 9x2 + (-36 + -12x + -1x2)

Reorder the terms:
9x2 = 36 + -36 + 36x + -12x + 9x2 + -1x2

Combine like terms: 36 + -36 = 0
9x2 = 0 + 36x + -12x + 9x2 + -1x2
9x2 = 36x + -12x + 9x2 + -1x2

Combine like terms: 36x + -12x = 24x
9x2 = 24x + 9x2 + -1x2

Combine like terms: 9x2 + -1x2 = 8x2
9x2 = 24x + 8x2

Solving
9x2 = 24x + 8x2

Solving for variable 'x'.

Reorder the terms:
-24x + 9x2 + -8x2 = 24x + 8x2 + -24x + -8x2

Combine like terms: 9x2 + -8x2 = 1x2
-24x + 1x2 = 24x + 8x2 + -24x + -8x2

Reorder the terms:
-24x + 1x2 = 24x + -24x + 8x2 + -8x2

Combine like terms: 24x + -24x = 0
-24x + 1x2 = 0 + 8x2 + -8x2
-24x + 1x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-24x + 1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-24 + x) = 0

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 '(-24 + x)' equal to zero and attempt to solve: Simplifying -24 + x = 0 Solving -24 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + x = 0 + 24 x = 0 + 24 Combine like terms: 0 + 24 = 24 x = 24 Simplifying x = 24

Solution

x = {0, 24}

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