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Simplifying 12w2 + w = 6 Reorder the terms: w + 12w2 = 6 Solving w + 12w2 = 6 Solving for variable 'w'. Reorder the terms: -6 + w + 12w2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + w + 12w2 = 0 Factor a trinomial. (-3 + -4w)(2 + -3w) = 0Subproblem 1
Set the factor '(-3 + -4w)' equal to zero and attempt to solve: Simplifying -3 + -4w = 0 Solving -3 + -4w = 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 + -4w = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4w = 0 + 3 -4w = 0 + 3 Combine like terms: 0 + 3 = 3 -4w = 3 Divide each side by '-4'. w = -0.75 Simplifying w = -0.75Subproblem 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 = {-0.75, 0.6666666667}
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