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Simplifying (w2 + 4w4)(w + -2w2)(w + 2w2) = 0 Multiply (w2 + 4w4) * (w + -2w2) (w2(w + -2w2) + 4w4 * (w + -2w2))(w + 2w2) = 0 ((w * w2 + -2w2 * w2) + 4w4 * (w + -2w2))(w + 2w2) = 0 ((w3 + -2w4) + 4w4 * (w + -2w2))(w + 2w2) = 0 (w3 + -2w4 + (w * 4w4 + -2w2 * 4w4))(w + 2w2) = 0 (w3 + -2w4 + (4w5 + -8w6))(w + 2w2) = 0 (w3 + -2w4 + 4w5 + -8w6)(w + 2w2) = 0 Multiply (w3 + -2w4 + 4w5 + -8w6) * (w + 2w2) (w3(w + 2w2) + -2w4 * (w + 2w2) + 4w5 * (w + 2w2) + -8w6 * (w + 2w2)) = 0 ((w * w3 + 2w2 * w3) + -2w4 * (w + 2w2) + 4w5 * (w + 2w2) + -8w6 * (w + 2w2)) = 0 ((w4 + 2w5) + -2w4 * (w + 2w2) + 4w5 * (w + 2w2) + -8w6 * (w + 2w2)) = 0 (w4 + 2w5 + (w * -2w4 + 2w2 * -2w4) + 4w5 * (w + 2w2) + -8w6 * (w + 2w2)) = 0 (w4 + 2w5 + (-2w5 + -4w6) + 4w5 * (w + 2w2) + -8w6 * (w + 2w2)) = 0 (w4 + 2w5 + -2w5 + -4w6 + (w * 4w5 + 2w2 * 4w5) + -8w6 * (w + 2w2)) = 0 (w4 + 2w5 + -2w5 + -4w6 + (4w6 + 8w7) + -8w6 * (w + 2w2)) = 0 (w4 + 2w5 + -2w5 + -4w6 + 4w6 + 8w7 + (w * -8w6 + 2w2 * -8w6)) = 0 (w4 + 2w5 + -2w5 + -4w6 + 4w6 + 8w7 + (-8w7 + -16w8)) = 0 Combine like terms: 2w5 + -2w5 = 0 (w4 + 0 + -4w6 + 4w6 + 8w7 + -8w7 + -16w8) = 0 (w4 + -4w6 + 4w6 + 8w7 + -8w7 + -16w8) = 0 Combine like terms: -4w6 + 4w6 = 0 (w4 + 0 + 8w7 + -8w7 + -16w8) = 0 (w4 + 8w7 + -8w7 + -16w8) = 0 Combine like terms: 8w7 + -8w7 = 0 (w4 + 0 + -16w8) = 0 (w4 + -16w8) = 0 Solving w4 + -16w8 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'w4'. w4(1 + -16w4) = 0 Factor a difference between two squares. w4((1 + 4w2)(1 + -4w2)) = 0 Factor a difference between two squares. w4((1 + 4w2)((1 + 2w)(1 + -2w))) = 0Subproblem 1
Set the factor 'w4' equal to zero and attempt to solve: Simplifying w4 = 0 Solving w4 = 0 Move all terms containing w to the left, all other terms to the right. Simplifying w4 = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(1 + 4w2)' equal to zero and attempt to solve: Simplifying 1 + 4w2 = 0 Solving 1 + 4w2 = 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 + 4w2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4w2 = 0 + -1 4w2 = 0 + -1 Combine like terms: 0 + -1 = -1 4w2 = -1 Divide each side by '4'. w2 = -0.25 Simplifying w2 = -0.25 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
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 = -0.5Subproblem 4
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 = 0.5Solution
w = {-0.5, 0.5}
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