(w-3)(w+7)=0

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Solution for (w-3)(w+7)=0 equation:


Simplifying
(w + -3)(w + 7) = 0

Reorder the terms:
(-3 + w)(w + 7) = 0

Reorder the terms:
(-3 + w)(7 + w) = 0

Multiply (-3 + w) * (7 + w)
(-3(7 + w) + w(7 + w)) = 0
((7 * -3 + w * -3) + w(7 + w)) = 0
((-21 + -3w) + w(7 + w)) = 0
(-21 + -3w + (7 * w + w * w)) = 0
(-21 + -3w + (7w + w2)) = 0

Combine like terms: -3w + 7w = 4w
(-21 + 4w + w2) = 0

Solving
-21 + 4w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-7 + -1w)(3 + -1w) = 0

Subproblem 1

Set the factor '(-7 + -1w)' equal to zero and attempt to solve: Simplifying -7 + -1w = 0 Solving -7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1w = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1w = 0 + 7 -1w = 0 + 7 Combine like terms: 0 + 7 = 7 -1w = 7 Divide each side by '-1'. w = -7 Simplifying w = -7

Subproblem 2

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

Solution

w = {-7, 3}

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