0=5x^2+10x-120

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Solution for 0=5x^2+10x-120 equation:


Simplifying
0 = 5x2 + 10x + -120

Reorder the terms:
0 = -120 + 10x + 5x2

Solving
0 = -120 + 10x + 5x2

Solving for variable 'x'.

Combine like terms: 0 + 120 = 120
120 + -10x + -5x2 = -120 + 10x + 5x2 + 120 + -10x + -5x2

Reorder the terms:
120 + -10x + -5x2 = -120 + 120 + 10x + -10x + 5x2 + -5x2

Combine like terms: -120 + 120 = 0
120 + -10x + -5x2 = 0 + 10x + -10x + 5x2 + -5x2
120 + -10x + -5x2 = 10x + -10x + 5x2 + -5x2

Combine like terms: 10x + -10x = 0
120 + -10x + -5x2 = 0 + 5x2 + -5x2
120 + -10x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
120 + -10x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(24 + -2x + -1x2) = 0

Factor a trinomial.
5((4 + -1x)(6 + x)) = 0

Ignore the factor 5.

Subproblem 1

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

Subproblem 2

Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6

Solution

x = {4, -6}

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