-6x^2-34x-64=-4x^2-18x-34

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Solution for -6x^2-34x-64=-4x^2-18x-34 equation:


Simplifying
-6x2 + -34x + -64 = -4x2 + -18x + -34

Reorder the terms:
-64 + -34x + -6x2 = -4x2 + -18x + -34

Reorder the terms:
-64 + -34x + -6x2 = -34 + -18x + -4x2

Solving
-64 + -34x + -6x2 = -34 + -18x + -4x2

Solving for variable 'x'.

Reorder the terms:
-64 + 34 + -34x + 18x + -6x2 + 4x2 = -34 + -18x + -4x2 + 34 + 18x + 4x2

Combine like terms: -64 + 34 = -30
-30 + -34x + 18x + -6x2 + 4x2 = -34 + -18x + -4x2 + 34 + 18x + 4x2

Combine like terms: -34x + 18x = -16x
-30 + -16x + -6x2 + 4x2 = -34 + -18x + -4x2 + 34 + 18x + 4x2

Combine like terms: -6x2 + 4x2 = -2x2
-30 + -16x + -2x2 = -34 + -18x + -4x2 + 34 + 18x + 4x2

Reorder the terms:
-30 + -16x + -2x2 = -34 + 34 + -18x + 18x + -4x2 + 4x2

Combine like terms: -34 + 34 = 0
-30 + -16x + -2x2 = 0 + -18x + 18x + -4x2 + 4x2
-30 + -16x + -2x2 = -18x + 18x + -4x2 + 4x2

Combine like terms: -18x + 18x = 0
-30 + -16x + -2x2 = 0 + -4x2 + 4x2
-30 + -16x + -2x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-30 + -16x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(15 + 8x + x2) = 0

Factor a trinomial.
-2((5 + x)(3 + x)) = 0

Ignore the factor -2.

Subproblem 1

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

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 = {-5, -3}

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