(x-12)(x+17)=0

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Solution for (x-12)(x+17)=0 equation:


Simplifying
(x + -12)(x + 17) = 0

Reorder the terms:
(-12 + x)(x + 17) = 0

Reorder the terms:
(-12 + x)(17 + x) = 0

Multiply (-12 + x) * (17 + x)
(-12(17 + x) + x(17 + x)) = 0
((17 * -12 + x * -12) + x(17 + x)) = 0
((-204 + -12x) + x(17 + x)) = 0
(-204 + -12x + (17 * x + x * x)) = 0
(-204 + -12x + (17x + x2)) = 0

Combine like terms: -12x + 17x = 5x
(-204 + 5x + x2) = 0

Solving
-204 + 5x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-17 + -1x)(12 + -1x) = 0

Subproblem 1

Set the factor '(-17 + -1x)' equal to zero and attempt to solve: Simplifying -17 + -1x = 0 Solving -17 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -1x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -1x = 0 + 17 -1x = 0 + 17 Combine like terms: 0 + 17 = 17 -1x = 17 Divide each side by '-1'. x = -17 Simplifying x = -17

Subproblem 2

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

Solution

x = {-17, 12}

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