12w^3+22w^2-20w=0

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Solution for 12w^3+22w^2-20w=0 equation:


Simplifying
12w3 + 22w2 + -20w = 0

Reorder the terms:
-20w + 22w2 + 12w3 = 0

Solving
-20w + 22w2 + 12w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2w'.
2w(-10 + 11w + 6w2) = 0

Factor a trinomial.
2w((-5 + -2w)(2 + -3w)) = 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 + -2w)' equal to zero and attempt to solve: Simplifying -5 + -2w = 0 Solving -5 + -2w = 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 + -2w = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2w = 0 + 5 -2w = 0 + 5 Combine like terms: 0 + 5 = 5 -2w = 5 Divide each side by '-2'. w = -2.5 Simplifying w = -2.5

Subproblem 3

Set the factor '(2 + -3w)' equal to zero and attempt to solve: Simplifying 2 + -3w = 0 Solving 2 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3w = 0 + -2 -3w = 0 + -2 Combine like terms: 0 + -2 = -2 -3w = -2 Divide each side by '-3'. w = 0.6666666667 Simplifying w = 0.6666666667

Solution

w = {0, -2.5, 0.6666666667}

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