w^2-w=36+4w

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Solution for w^2-w=36+4w equation:


Simplifying
w2 + -1w = 36 + 4w

Reorder the terms:
-1w + w2 = 36 + 4w

Solving
-1w + w2 = 36 + 4w

Solving for variable 'w'.

Reorder the terms:
-36 + -1w + -4w + w2 = 36 + 4w + -36 + -4w

Combine like terms: -1w + -4w = -5w
-36 + -5w + w2 = 36 + 4w + -36 + -4w

Reorder the terms:
-36 + -5w + w2 = 36 + -36 + 4w + -4w

Combine like terms: 36 + -36 = 0
-36 + -5w + w2 = 0 + 4w + -4w
-36 + -5w + w2 = 4w + -4w

Combine like terms: 4w + -4w = 0
-36 + -5w + w2 = 0

Factor a trinomial.
(-4 + -1w)(9 + -1w) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(9 + -1w)' equal to zero and attempt to solve: Simplifying 9 + -1w = 0 Solving 9 + -1w = 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 + -1w = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1w = 0 + -9 -1w = 0 + -9 Combine like terms: 0 + -9 = -9 -1w = -9 Divide each side by '-1'. w = 9 Simplifying w = 9

Solution

w = {-4, 9}

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