(120-10x)(6+x)=0

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Solution for (120-10x)(6+x)=0 equation:


Simplifying
(120 + -10x)(6 + x) = 0

Multiply (120 + -10x) * (6 + x)
(120(6 + x) + -10x * (6 + x)) = 0
((6 * 120 + x * 120) + -10x * (6 + x)) = 0
((720 + 120x) + -10x * (6 + x)) = 0
(720 + 120x + (6 * -10x + x * -10x)) = 0
(720 + 120x + (-60x + -10x2)) = 0

Combine like terms: 120x + -60x = 60x
(720 + 60x + -10x2) = 0

Solving
720 + 60x + -10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(72 + 6x + -1x2) = 0

Factor a trinomial.
10((12 + -1x)(6 + x)) = 0

Ignore the factor 10.

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 '(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 = {12, -6}

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