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Simplifying 0 = 3w2 + 14w + 8 Reorder the terms: 0 = 8 + 14w + 3w2 Solving 0 = 8 + 14w + 3w2 Solving for variable 'w'. Combine like terms: 0 + -8 = -8 -8 + -14w + -3w2 = 8 + 14w + 3w2 + -8 + -14w + -3w2 Reorder the terms: -8 + -14w + -3w2 = 8 + -8 + 14w + -14w + 3w2 + -3w2 Combine like terms: 8 + -8 = 0 -8 + -14w + -3w2 = 0 + 14w + -14w + 3w2 + -3w2 -8 + -14w + -3w2 = 14w + -14w + 3w2 + -3w2 Combine like terms: 14w + -14w = 0 -8 + -14w + -3w2 = 0 + 3w2 + -3w2 -8 + -14w + -3w2 = 3w2 + -3w2 Combine like terms: 3w2 + -3w2 = 0 -8 + -14w + -3w2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 14w + 3w2) = 0 Factor a trinomial. -1((4 + w)(2 + 3w)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + w)' equal to zero and attempt to solve: Simplifying 4 + w = 0 Solving 4 + w = 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 + w = 0 + -4 Combine like terms: 4 + -4 = 0 0 + w = 0 + -4 w = 0 + -4 Combine like terms: 0 + -4 = -4 w = -4 Simplifying w = -4Subproblem 2
Set the factor '(2 + 3w)' equal to zero and attempt to solve: Simplifying 2 + 3w = 0 Solving 2 + 3w = 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 + 3w = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3w = 0 + -2 3w = 0 + -2 Combine like terms: 0 + -2 = -2 3w = -2 Divide each side by '3'. w = -0.6666666667 Simplifying w = -0.6666666667Solution
w = {-4, -0.6666666667}
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