4x^2-57=5x^2+22x

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Solution for 4x^2-57=5x^2+22x equation:


Simplifying
4x2 + -57 = 5x2 + 22x

Reorder the terms:
-57 + 4x2 = 5x2 + 22x

Reorder the terms:
-57 + 4x2 = 22x + 5x2

Solving
-57 + 4x2 = 22x + 5x2

Solving for variable 'x'.

Reorder the terms:
-57 + -22x + 4x2 + -5x2 = 22x + 5x2 + -22x + -5x2

Combine like terms: 4x2 + -5x2 = -1x2
-57 + -22x + -1x2 = 22x + 5x2 + -22x + -5x2

Reorder the terms:
-57 + -22x + -1x2 = 22x + -22x + 5x2 + -5x2

Combine like terms: 22x + -22x = 0
-57 + -22x + -1x2 = 0 + 5x2 + -5x2
-57 + -22x + -1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-57 + -22x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(57 + 22x + x2) = 0

Factor a trinomial.
-1((19 + x)(3 + x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(19 + x)' equal to zero and attempt to solve: Simplifying 19 + x = 0 Solving 19 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 0 + -19 Combine like terms: 19 + -19 = 0 0 + x = 0 + -19 x = 0 + -19 Combine like terms: 0 + -19 = -19 x = -19 Simplifying x = -19

Subproblem 2

Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 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 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3

Solution

x = {-19, -3}

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