(w+3)(w-12)=0

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Solution for (w+3)(w-12)=0 equation:


Simplifying
(w + 3)(w + -12) = 0

Reorder the terms:
(3 + w)(w + -12) = 0

Reorder the terms:
(3 + w)(-12 + w) = 0

Multiply (3 + w) * (-12 + w)
(3(-12 + w) + w(-12 + w)) = 0
((-12 * 3 + w * 3) + w(-12 + w)) = 0
((-36 + 3w) + w(-12 + w)) = 0
(-36 + 3w + (-12 * w + w * w)) = 0
(-36 + 3w + (-12w + w2)) = 0

Combine like terms: 3w + -12w = -9w
(-36 + -9w + w2) = 0

Solving
-36 + -9w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-3 + -1w)(12 + -1w) = 0

Subproblem 1

Set the factor '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3

Subproblem 2

Set the factor '(12 + -1w)' equal to zero and attempt to solve: Simplifying 12 + -1w = 0 Solving 12 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1w = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1w = 0 + -12 -1w = 0 + -12 Combine like terms: 0 + -12 = -12 -1w = -12 Divide each side by '-1'. w = 12 Simplifying w = 12

Solution

w = {-3, 12}

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