-30w^2=3w^3+75w

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Solution for -30w^2=3w^3+75w equation:


Simplifying
-30w2 = 3w3 + 75w

Reorder the terms:
-30w2 = 75w + 3w3

Solving
-30w2 = 75w + 3w3

Solving for variable 'w'.

Reorder the terms:
-75w + -30w2 + -3w3 = 75w + 3w3 + -75w + -3w3

Reorder the terms:
-75w + -30w2 + -3w3 = 75w + -75w + 3w3 + -3w3

Combine like terms: 75w + -75w = 0
-75w + -30w2 + -3w3 = 0 + 3w3 + -3w3
-75w + -30w2 + -3w3 = 3w3 + -3w3

Combine like terms: 3w3 + -3w3 = 0
-75w + -30w2 + -3w3 = 0

Factor out the Greatest Common Factor (GCF), '-3w'.
-3w(25 + 10w + w2) = 0

Factor a trinomial.
-3w((5 + w)(5 + w)) = 0

Ignore the factor -3.

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 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 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 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5

Subproblem 3

Set the factor '(5 + w)' equal to zero and attempt to solve: Simplifying 5 + w = 0 Solving 5 + w = 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 + w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + w = 0 + -5 w = 0 + -5 Combine like terms: 0 + -5 = -5 w = -5 Simplifying w = -5

Solution

w = {0, -5, -5}

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