(w-3)(w+5)=9

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Solution for (w-3)(w+5)=9 equation:


Simplifying
(w + -3)(w + 5) = 9

Reorder the terms:
(-3 + w)(w + 5) = 9

Reorder the terms:
(-3 + w)(5 + w) = 9

Multiply (-3 + w) * (5 + w)
(-3(5 + w) + w(5 + w)) = 9
((5 * -3 + w * -3) + w(5 + w)) = 9
((-15 + -3w) + w(5 + w)) = 9
(-15 + -3w + (5 * w + w * w)) = 9
(-15 + -3w + (5w + w2)) = 9

Combine like terms: -3w + 5w = 2w
(-15 + 2w + w2) = 9

Solving
-15 + 2w + w2 = 9

Solving for variable 'w'.

Reorder the terms:
-15 + -9 + 2w + w2 = 9 + -9

Combine like terms: -15 + -9 = -24
-24 + 2w + w2 = 9 + -9

Combine like terms: 9 + -9 = 0
-24 + 2w + w2 = 0

Factor a trinomial.
(-6 + -1w)(4 + -1w) = 0

Subproblem 1

Set the factor '(-6 + -1w)' equal to zero and attempt to solve: Simplifying -6 + -1w = 0 Solving -6 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1w = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1w = 0 + 6 -1w = 0 + 6 Combine like terms: 0 + 6 = 6 -1w = 6 Divide each side by '-1'. w = -6 Simplifying w = -6

Subproblem 2

Set the factor '(4 + -1w)' equal to zero and attempt to solve: Simplifying 4 + -1w = 0 Solving 4 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1w = 0 + -4 -1w = 0 + -4 Combine like terms: 0 + -4 = -4 -1w = -4 Divide each side by '-1'. w = 4 Simplifying w = 4

Solution

w = {-6, 4}

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