(8-w)(4w-90)=0

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Solution for (8-w)(4w-90)=0 equation: 


Simplifying
(8 + -1w)(4w + -90) = 0

Reorder the terms:
(8 + -1w)(-90 + 4w) = 0

Multiply (8 + -1w) * (-90 + 4w)
(8(-90 + 4w) + -1w * (-90 + 4w)) = 0
((-90 * 8 + 4w * 8) + -1w * (-90 + 4w)) = 0
((-720 + 32w) + -1w * (-90 + 4w)) = 0
(-720 + 32w + (-90 * -1w + 4w * -1w)) = 0
(-720 + 32w + (90w + -4w2)) = 0

Combine like terms: 32w + 90w = 122w
(-720 + 122w + -4w2) = 0

Solving
-720 + 122w + -4w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-360 + 61w + -2w2) = 0

Factor a trinomial.
2((-45 + 2w)(8 + -1w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-45 + 2w)' equal to zero and attempt to solve:

Simplifying
-45 + 2w = 0

Solving
-45 + 2w = 0

Move all terms containing w to the left, all other terms to the right.

Add '45' to each side of the equation.
-45 + 45 + 2w = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 2w = 0 + 45
2w = 0 + 45

Combine like terms: 0 + 45 = 45
2w = 45

Divide each side by '2'.
w = 22.5

Simplifying
w = 22.5

Subproblem 2
Set the factor '(8 + -1w)' equal to zero and attempt to solve:

Simplifying
8 + -1w = 0

Solving
8 + -1w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -1w = 0 + -8

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

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

Divide each side by '-1'.
w = 8

Simplifying
w = 8
Solution
w = {22.5, 8}

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