(3x+6)*(x-3)=9*(9+3x+2)

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Solution for (3x+6)*(x-3)=9*(9+3x+2) equation:


Simplifying
(3x + 6)(x + -3) = 9(9 + 3x + 2)

Reorder the terms:
(6 + 3x)(x + -3) = 9(9 + 3x + 2)

Reorder the terms:
(6 + 3x)(-3 + x) = 9(9 + 3x + 2)

Multiply (6 + 3x) * (-3 + x)
(6(-3 + x) + 3x * (-3 + x)) = 9(9 + 3x + 2)
((-3 * 6 + x * 6) + 3x * (-3 + x)) = 9(9 + 3x + 2)
((-18 + 6x) + 3x * (-3 + x)) = 9(9 + 3x + 2)
(-18 + 6x + (-3 * 3x + x * 3x)) = 9(9 + 3x + 2)
(-18 + 6x + (-9x + 3x2)) = 9(9 + 3x + 2)

Combine like terms: 6x + -9x = -3x
(-18 + -3x + 3x2) = 9(9 + 3x + 2)

Reorder the terms:
-18 + -3x + 3x2 = 9(9 + 2 + 3x)

Combine like terms: 9 + 2 = 11
-18 + -3x + 3x2 = 9(11 + 3x)
-18 + -3x + 3x2 = (11 * 9 + 3x * 9)
-18 + -3x + 3x2 = (99 + 27x)

Solving
-18 + -3x + 3x2 = 99 + 27x

Solving for variable 'x'.

Reorder the terms:
-18 + -99 + -3x + -27x + 3x2 = 99 + 27x + -99 + -27x

Combine like terms: -18 + -99 = -117
-117 + -3x + -27x + 3x2 = 99 + 27x + -99 + -27x

Combine like terms: -3x + -27x = -30x
-117 + -30x + 3x2 = 99 + 27x + -99 + -27x

Reorder the terms:
-117 + -30x + 3x2 = 99 + -99 + 27x + -27x

Combine like terms: 99 + -99 = 0
-117 + -30x + 3x2 = 0 + 27x + -27x
-117 + -30x + 3x2 = 27x + -27x

Combine like terms: 27x + -27x = 0
-117 + -30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-39 + -10x + x2) = 0

Factor a trinomial.
3((-3 + -1x)(13 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13

Solution

x = {-3, 13}

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