4x^2-112=5x^2+22x

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Solution for 4x^2-112=5x^2+22x equation:


Simplifying
4x2 + -112 = 5x2 + 22x

Reorder the terms:
-112 + 4x2 = 5x2 + 22x

Reorder the terms:
-112 + 4x2 = 22x + 5x2

Solving
-112 + 4x2 = 22x + 5x2

Solving for variable 'x'.

Reorder the terms:
-112 + -22x + 4x2 + -5x2 = 22x + 5x2 + -22x + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
-112 + -22x + -1x2 = 22x + 5x2 + -22x + -5x2

Reorder the terms:
-112 + -22x + -1x2 = 22x + -22x + 5x2 + -5x2

Combine like terms: 22x + -22x = 0
-112 + -22x + -1x2 = 0 + 5x2 + -5x2
-112 + -22x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-112 + -22x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(112 + 22x + x2) = 0

Factor a trinomial.
-1((14 + x)(8 + x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Simplifying x = -14

Subproblem 2

Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8

Solution

x = {-14, -8}

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