w^2-13=4w+8

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Solution for w^2-13=4w+8 equation: 


Simplifying
w2 + -13 = 4w + 8

Reorder the terms:
-13 + w2 = 4w + 8

Reorder the terms:
-13 + w2 = 8 + 4w

Solving
-13 + w2 = 8 + 4w

Solving for variable 'w'.

Reorder the terms:
-13 + -8 + -4w + w2 = 8 + 4w + -8 + -4w

Combine like terms: -13 + -8 = -21
-21 + -4w + w2 = 8 + 4w + -8 + -4w

Reorder the terms:
-21 + -4w + w2 = 8 + -8 + 4w + -4w

Combine like terms: 8 + -8 = 0
-21 + -4w + w2 = 0 + 4w + -4w
-21 + -4w + w2 = 4w + -4w

Combine like terms: 4w + -4w = 0
-21 + -4w + w2 = 0

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


Subproblem 1
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

Subproblem 2
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
Solution
w = {-3, 7}

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