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Simplifying (5w + -6) * x(9 + -1w) = 0 Reorder the terms: (-6 + 5w) * x(9 + -1w) = 0 Reorder the terms for easier multiplication: x(-6 + 5w)(9 + -1w) = 0 Multiply (-6 + 5w) * (9 + -1w) x(-6(9 + -1w) + 5w * (9 + -1w)) = 0 x((9 * -6 + -1w * -6) + 5w * (9 + -1w)) = 0 x((-54 + 6w) + 5w * (9 + -1w)) = 0 x(-54 + 6w + (9 * 5w + -1w * 5w)) = 0 x(-54 + 6w + (45w + -5w2)) = 0 Combine like terms: 6w + 45w = 51w x(-54 + 51w + -5w2) = 0 (-54 * x + 51w * x + -5w2 * x) = 0 Reorder the terms: (51wx + -5w2x + -54x) = 0 (51wx + -5w2x + -54x) = 0 Solving 51wx + -5w2x + -54x = 0 Solving for variable 'w'. Factor out the Greatest Common Factor (GCF), 'x'. x(51w + -5w2 + -54) = 0 Factor a trinomial. x((-5w + 6)(w + -9)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing w to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x 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 '(-5w + 6)' equal to zero and attempt to solve: Simplifying -5w + 6 = 0 Reorder the terms: 6 + -5w = 0 Solving 6 + -5w = 0 Move all terms containing w to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5w = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5w = 0 + -6 -5w = 0 + -6 Combine like terms: 0 + -6 = -6 -5w = -6 Divide each side by '-5'. w = 1.2 Simplifying w = 1.2Subproblem 3
Set the factor '(w + -9)' equal to zero and attempt to solve: Simplifying w + -9 = 0 Reorder the terms: -9 + w = 0 Solving -9 + w = 0 Move all terms containing w to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + w = 0 + 9 Combine like terms: -9 + 9 = 0 0 + w = 0 + 9 w = 0 + 9 Combine like terms: 0 + 9 = 9 w = 9 Simplifying w = 9Solution
w = {1.2, 9}
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