32w^2+32w+8=0

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Solution for 32w^2+32w+8=0 equation:


Simplifying
32w2 + 32w + 8 = 0

Reorder the terms:
8 + 32w + 32w2 = 0

Solving
8 + 32w + 32w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + 4w + 4w2) = 0

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

Ignore the factor 8.

Subproblem 1

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 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

Solution

w = {-0.5, -0.5}

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