w^2+5w-32=2w-4

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Solution for w^2+5w-32=2w-4 equation: 


Simplifying
w2 + 5w + -32 = 2w + -4

Reorder the terms:
-32 + 5w + w2 = 2w + -4

Reorder the terms:
-32 + 5w + w2 = -4 + 2w

Solving
-32 + 5w + w2 = -4 + 2w

Solving for variable 'w'.

Reorder the terms:
-32 + 4 + 5w + -2w + w2 = -4 + 2w + 4 + -2w

Combine like terms: -32 + 4 = -28
-28 + 5w + -2w + w2 = -4 + 2w + 4 + -2w

Combine like terms: 5w + -2w = 3w
-28 + 3w + w2 = -4 + 2w + 4 + -2w

Reorder the terms:
-28 + 3w + w2 = -4 + 4 + 2w + -2w

Combine like terms: -4 + 4 = 0
-28 + 3w + w2 = 0 + 2w + -2w
-28 + 3w + w2 = 2w + -2w

Combine like terms: 2w + -2w = 0
-28 + 3w + w2 = 0

Factor a trinomial.
(-7 + -1w)(4 + -1w) = 0


Subproblem 1
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

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 = {-7, 4}

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