2x^2+14x=120

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Solution for 2x^2+14x=120 equation:

Simplifying
2x2 + 14x = 120

Reorder the terms:
14x + 2x2 = 120

Solving
14x + 2x2 = 120

Solving for variable 'x'.

Reorder the terms:
-120 + 14x + 2x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-120 + 14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-60 + 7x + x2) = 0

Factor a trinomial.
2((-12 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12

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

x = {-12, 5}