40w^3+36w^2+8w=0

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Solution for 40w^3+36w^2+8w=0 equation:


Simplifying
40w3 + 36w2 + 8w = 0

Reorder the terms:
8w + 36w2 + 40w3 = 0

Solving
8w + 36w2 + 40w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '4w'.
4w(2 + 9w + 10w2) = 0

Factor a trinomial.
4w((1 + 2w)(2 + 5w)) = 0

Ignore the factor 4.

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 '(1 + 2w)' equal to zero and attempt to solve: Simplifying 1 + 2w = 0 Solving 1 + 2w = 0 Move all terms containing w to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 2w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 2w = 0 + -1 2w = 0 + -1 Combine like terms: 0 + -1 = -1 2w = -1 Divide each side by '2'. w = -0.5 Simplifying w = -0.5

Subproblem 3

Set the factor '(2 + 5w)' equal to zero and attempt to solve: Simplifying 2 + 5w = 0 Solving 2 + 5w = 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 + 5w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5w = 0 + -2 5w = 0 + -2 Combine like terms: 0 + -2 = -2 5w = -2 Divide each side by '5'. w = -0.4 Simplifying w = -0.4

Solution

w = {0, -0.5, -0.4}

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