8(x^2-6)+9x=3x(3x+7)-13

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Solution for 8(x^2-6)+9x=3x(3x+7)-13 equation:


Simplifying
8(x2 + -6) + 9x = 3x(3x + 7) + -13

Reorder the terms:
8(-6 + x2) + 9x = 3x(3x + 7) + -13
(-6 * 8 + x2 * 8) + 9x = 3x(3x + 7) + -13
(-48 + 8x2) + 9x = 3x(3x + 7) + -13

Reorder the terms:
-48 + 9x + 8x2 = 3x(3x + 7) + -13

Reorder the terms:
-48 + 9x + 8x2 = 3x(7 + 3x) + -13
-48 + 9x + 8x2 = (7 * 3x + 3x * 3x) + -13
-48 + 9x + 8x2 = (21x + 9x2) + -13

Reorder the terms:
-48 + 9x + 8x2 = -13 + 21x + 9x2

Solving
-48 + 9x + 8x2 = -13 + 21x + 9x2

Solving for variable 'x'.

Reorder the terms:
-48 + 13 + 9x + -21x + 8x2 + -9x2 = -13 + 21x + 9x2 + 13 + -21x + -9x2

Combine like terms: -48 + 13 = -35
-35 + 9x + -21x + 8x2 + -9x2 = -13 + 21x + 9x2 + 13 + -21x + -9x2

Combine like terms: 9x + -21x = -12x
-35 + -12x + 8x2 + -9x2 = -13 + 21x + 9x2 + 13 + -21x + -9x2

Combine like terms: 8x2 + -9x2 = -1x2
-35 + -12x + -1x2 = -13 + 21x + 9x2 + 13 + -21x + -9x2

Reorder the terms:
-35 + -12x + -1x2 = -13 + 13 + 21x + -21x + 9x2 + -9x2

Combine like terms: -13 + 13 = 0
-35 + -12x + -1x2 = 0 + 21x + -21x + 9x2 + -9x2
-35 + -12x + -1x2 = 21x + -21x + 9x2 + -9x2

Combine like terms: 21x + -21x = 0
-35 + -12x + -1x2 = 0 + 9x2 + -9x2
-35 + -12x + -1x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-35 + -12x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(35 + 12x + x2) = 0

Factor a trinomial.
-1((7 + x)(5 + x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5

Solution

x = {-7, -5}

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