2x^2-6x-15=5

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Solution for 2x^2-6x-15=5 equation:


Simplifying
2x2 + -6x + -15 = 5

Reorder the terms:
-15 + -6x + 2x2 = 5

Solving
-15 + -6x + 2x2 = 5

Solving for variable 'x'.

Reorder the terms:
-15 + -5 + -6x + 2x2 = 5 + -5

Combine like terms: -15 + -5 = -20
-20 + -6x + 2x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-20 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -3x + x2) = 0

Factor a trinomial.
2((-2 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

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 '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {-2, 5}

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