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Simplifying 10w6 + 26w5 + -12w4 = 0 Reorder the terms: -12w4 + 26w5 + 10w6 = 0 Solving -12w4 + 26w5 + 10w6 = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), '2w4'. 2w4(-6 + 13w + 5w2) = 0 Factor a trinomial. 2w4((-3 + -1w)(2 + -5w)) = 0 Ignore the factor 2.Subproblem 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 '(-3 + -1w)' equal to zero and attempt to solve: Simplifying -3 + -1w = 0 Solving -3 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1w = 0 + 3 -1w = 0 + 3 Combine like terms: 0 + 3 = 3 -1w = 3 Divide each side by '-1'. w = -3 Simplifying w = -3Subproblem 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 = 0.4Solution
w = {-3, 0.4}
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