8x^2-7x-50=2x^2+5x-2

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Solution for 8x^2-7x-50=2x^2+5x-2 equation:


Simplifying
8x2 + -7x + -50 = 2x2 + 5x + -2

Reorder the terms:
-50 + -7x + 8x2 = 2x2 + 5x + -2

Reorder the terms:
-50 + -7x + 8x2 = -2 + 5x + 2x2

Solving
-50 + -7x + 8x2 = -2 + 5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-50 + 2 + -7x + -5x + 8x2 + -2x2 = -2 + 5x + 2x2 + 2 + -5x + -2x2

Combine like terms: -50 + 2 = -48
-48 + -7x + -5x + 8x2 + -2x2 = -2 + 5x + 2x2 + 2 + -5x + -2x2

Combine like terms: -7x + -5x = -12x
-48 + -12x + 8x2 + -2x2 = -2 + 5x + 2x2 + 2 + -5x + -2x2

Combine like terms: 8x2 + -2x2 = 6x2
-48 + -12x + 6x2 = -2 + 5x + 2x2 + 2 + -5x + -2x2

Reorder the terms:
-48 + -12x + 6x2 = -2 + 2 + 5x + -5x + 2x2 + -2x2

Combine like terms: -2 + 2 = 0
-48 + -12x + 6x2 = 0 + 5x + -5x + 2x2 + -2x2
-48 + -12x + 6x2 = 5x + -5x + 2x2 + -2x2

Combine like terms: 5x + -5x = 0
-48 + -12x + 6x2 = 0 + 2x2 + -2x2
-48 + -12x + 6x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-48 + -12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-8 + -2x + x2) = 0

Factor a trinomial.
6((-2 + -1x)(4 + -1x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

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 = {-2, 4}

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