0=w^2+4w-45

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Solution for 0=w^2+4w-45 equation:


Simplifying
0 = w2 + 4w + -45

Reorder the terms:
0 = -45 + 4w + w2

Solving
0 = -45 + 4w + w2

Solving for variable 'w'.

Combine like terms: 0 + 45 = 45
45 + -4w + -1w2 = -45 + 4w + w2 + 45 + -4w + -1w2

Reorder the terms:
45 + -4w + -1w2 = -45 + 45 + 4w + -4w + w2 + -1w2

Combine like terms: -45 + 45 = 0
45 + -4w + -1w2 = 0 + 4w + -4w + w2 + -1w2
45 + -4w + -1w2 = 4w + -4w + w2 + -1w2

Combine like terms: 4w + -4w = 0
45 + -4w + -1w2 = 0 + w2 + -1w2
45 + -4w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
45 + -4w + -1w2 = 0

Factor a trinomial.
(5 + -1w)(9 + w) = 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 '(9 + w)' equal to zero and attempt to solve: Simplifying 9 + w = 0 Solving 9 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + w = 0 + -9 w = 0 + -9 Combine like terms: 0 + -9 = -9 w = -9 Simplifying w = -9

Solution

w = {5, -9}

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