(x)(5x-10)=120

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Solution for (x)(5x-10)=120 equation:


Simplifying
(x)(5x + -10) = 120

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

Solving
-10x + 5x2 = 120

Solving for variable 'x'.

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

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

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

Factor a trinomial.
5((-4 + -1x)(6 + -1x)) = 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 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6

Solution

x = {-4, 6}

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