(w-3)(w+4)=8

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Solution for (w-3)(w+4)=8 equation:


Simplifying
(w + -3)(w + 4) = 8

Reorder the terms:
(-3 + w)(w + 4) = 8

Reorder the terms:
(-3 + w)(4 + w) = 8

Multiply (-3 + w) * (4 + w)
(-3(4 + w) + w(4 + w)) = 8
((4 * -3 + w * -3) + w(4 + w)) = 8
((-12 + -3w) + w(4 + w)) = 8
(-12 + -3w + (4 * w + w * w)) = 8
(-12 + -3w + (4w + w2)) = 8

Combine like terms: -3w + 4w = 1w
(-12 + 1w + w2) = 8

Solving
-12 + 1w + w2 = 8

Solving for variable 'w'.

Reorder the terms:
-12 + -8 + 1w + w2 = 8 + -8

Combine like terms: -12 + -8 = -20
-20 + 1w + w2 = 8 + -8

Combine like terms: 8 + -8 = 0
-20 + 1w + w2 = 0

Factor a trinomial.
(-5 + -1w)(4 + -1w) = 0

Subproblem 1

Set the factor '(-5 + -1w)' equal to zero and attempt to solve: Simplifying -5 + -1w = 0 Solving -5 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1w = 0 + 5 -1w = 0 + 5 Combine like terms: 0 + 5 = 5 -1w = 5 Divide each side by '-1'. w = -5 Simplifying w = -5

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 = {-5, 4}

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