2w^2(w-4)=90w

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Solution for 2w^2(w-4)=90w equation: 


Simplifying
2w2(w + -4) = 90w

Reorder the terms:
2w2(-4 + w) = 90w
(-4 * 2w2 + w * 2w2) = 90w
(-8w2 + 2w3) = 90w

Solving
-8w2 + 2w3 = 90w

Solving for variable 'w'.

Reorder the terms:
-90w + -8w2 + 2w3 = 90w + -90w

Combine like terms: 90w + -90w = 0
-90w + -8w2 + 2w3 = 0

Factor out the Greatest Common Factor (GCF), '2w'.
2w(-45 + -4w + w2) = 0

Factor a trinomial.
2w((-5 + -1w)(9 + -1w)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0

Subproblem 2
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 3
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 = {0, -5, 9}

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