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Simplifying (w + 12)(6w + -1) = 0 Reorder the terms: (12 + w)(6w + -1) = 0 Reorder the terms: (12 + w)(-1 + 6w) = 0 Multiply (12 + w) * (-1 + 6w) (12(-1 + 6w) + w(-1 + 6w)) = 0 ((-1 * 12 + 6w * 12) + w(-1 + 6w)) = 0 ((-12 + 72w) + w(-1 + 6w)) = 0 (-12 + 72w + (-1 * w + 6w * w)) = 0 (-12 + 72w + (-1w + 6w2)) = 0 Combine like terms: 72w + -1w = 71w (-12 + 71w + 6w2) = 0 Solving -12 + 71w + 6w2 = 0 Solving for variable 'w'. Factor a trinomial. (-12 + -1w)(1 + -6w) = 0Subproblem 1
Set the factor '(-12 + -1w)' equal to zero and attempt to solve: Simplifying -12 + -1w = 0 Solving -12 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1w = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1w = 0 + 12 -1w = 0 + 12 Combine like terms: 0 + 12 = 12 -1w = 12 Divide each side by '-1'. w = -12 Simplifying w = -12Subproblem 2
Set the factor '(1 + -6w)' equal to zero and attempt to solve: Simplifying 1 + -6w = 0 Solving 1 + -6w = 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 + -6w = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -6w = 0 + -1 -6w = 0 + -1 Combine like terms: 0 + -1 = -1 -6w = -1 Divide each side by '-6'. w = 0.1666666667 Simplifying w = 0.1666666667Solution
w = {-12, 0.1666666667}
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