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Simplifying 4w * 3w + 2w = 24 Reorder the terms for easier multiplication: 4 * 3w * w + 2w = 24 Multiply 4 * 3 12w * w + 2w = 24 Multiply w * w 12w2 + 2w = 24 Reorder the terms: 2w + 12w2 = 24 Solving 2w + 12w2 = 24 Solving for variable 'w'. Reorder the terms: -24 + 2w + 12w2 = 24 + -24 Combine like terms: 24 + -24 = 0 -24 + 2w + 12w2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + w + 6w2) = 0 Factor a trinomial. 2((-3 + -2w)(4 + -3w)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + -2w)' equal to zero and attempt to solve: Simplifying -3 + -2w = 0 Solving -3 + -2w = 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 + -2w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2w = 0 + 3 -2w = 0 + 3 Combine like terms: 0 + 3 = 3 -2w = 3 Divide each side by '-2'. w = -1.5 Simplifying w = -1.5Subproblem 2
Set the factor '(4 + -3w)' equal to zero and attempt to solve: Simplifying 4 + -3w = 0 Solving 4 + -3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3w = 0 + -4 -3w = 0 + -4 Combine like terms: 0 + -4 = -4 -3w = -4 Divide each side by '-3'. w = 1.333333333 Simplifying w = 1.333333333Solution
w = {-1.5, 1.333333333}
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