(x-5)(x+12)=0

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Solution for (x-5)(x+12)=0 equation:


Simplifying
(x + -5)(x + 12) = 0

Reorder the terms:
(-5 + x)(x + 12) = 0

Reorder the terms:
(-5 + x)(12 + x) = 0

Multiply (-5 + x) * (12 + x)
(-5(12 + x) + x(12 + x)) = 0
((12 * -5 + x * -5) + x(12 + x)) = 0
((-60 + -5x) + x(12 + x)) = 0
(-60 + -5x + (12 * x + x * x)) = 0
(-60 + -5x + (12x + x2)) = 0

Combine like terms: -5x + 12x = 7x
(-60 + 7x + x2) = 0

Solving
-60 + 7x + x2 = 0

Solving for variable 'x'.

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

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

Solution

x = {-12, 5}

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