x^2+23x-138=8x-4x^2+2

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Solution for x^2+23x-138=8x-4x^2+2 equation:


Simplifying
x2 + 23x + -138 = 8x + -4x2 + 2

Reorder the terms:
-138 + 23x + x2 = 8x + -4x2 + 2

Reorder the terms:
-138 + 23x + x2 = 2 + 8x + -4x2

Solving
-138 + 23x + x2 = 2 + 8x + -4x2

Solving for variable 'x'.

Reorder the terms:
-138 + -2 + 23x + -8x + x2 + 4x2 = 2 + 8x + -4x2 + -2 + -8x + 4x2

Combine like terms: -138 + -2 = -140
-140 + 23x + -8x + x2 + 4x2 = 2 + 8x + -4x2 + -2 + -8x + 4x2

Combine like terms: 23x + -8x = 15x
-140 + 15x + x2 + 4x2 = 2 + 8x + -4x2 + -2 + -8x + 4x2

Combine like terms: x2 + 4x2 = 5x2
-140 + 15x + 5x2 = 2 + 8x + -4x2 + -2 + -8x + 4x2

Reorder the terms:
-140 + 15x + 5x2 = 2 + -2 + 8x + -8x + -4x2 + 4x2

Combine like terms: 2 + -2 = 0
-140 + 15x + 5x2 = 0 + 8x + -8x + -4x2 + 4x2
-140 + 15x + 5x2 = 8x + -8x + -4x2 + 4x2

Combine like terms: 8x + -8x = 0
-140 + 15x + 5x2 = 0 + -4x2 + 4x2
-140 + 15x + 5x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-140 + 15x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-28 + 3x + x2) = 0

Factor a trinomial.
5((-7 + -1x)(4 + -1x)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-7, 4}

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