15x^2-9x-31=-7

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Solution for 15x^2-9x-31=-7 equation:


Simplifying
15x2 + -9x + -31 = -7

Reorder the terms:
-31 + -9x + 15x2 = -7

Solving
-31 + -9x + 15x2 = -7

Solving for variable 'x'.

Reorder the terms:
-31 + 7 + -9x + 15x2 = -7 + 7

Combine like terms: -31 + 7 = -24
-24 + -9x + 15x2 = -7 + 7

Combine like terms: -7 + 7 = 0
-24 + -9x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + -3x + 5x2) = 0

Factor a trinomial.
3((-1 + -1x)(8 + -5x)) = 0

Ignore the factor 3.

Subproblem 1

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

Subproblem 2

Set the factor '(8 + -5x)' equal to zero and attempt to solve: Simplifying 8 + -5x = 0 Solving 8 + -5x = 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 + -5x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -5x = 0 + -8 -5x = 0 + -8 Combine like terms: 0 + -8 = -8 -5x = -8 Divide each side by '-5'. x = 1.6 Simplifying x = 1.6

Solution

x = {-1, 1.6}

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