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Simplifying (7 + -1w)(3w + 5) = 0 Reorder the terms: (7 + -1w)(5 + 3w) = 0 Multiply (7 + -1w) * (5 + 3w) (7(5 + 3w) + -1w * (5 + 3w)) = 0 ((5 * 7 + 3w * 7) + -1w * (5 + 3w)) = 0 ((35 + 21w) + -1w * (5 + 3w)) = 0 (35 + 21w + (5 * -1w + 3w * -1w)) = 0 (35 + 21w + (-5w + -3w2)) = 0 Combine like terms: 21w + -5w = 16w (35 + 16w + -3w2) = 0 Solving 35 + 16w + -3w2 = 0 Solving for variable 'w'. Factor a trinomial. (7 + -1w)(5 + 3w) = 0Subproblem 1
Set the factor '(7 + -1w)' equal to zero and attempt to solve: Simplifying 7 + -1w = 0 Solving 7 + -1w = 0 Move all terms containing w to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1w = 0 + -7 -1w = 0 + -7 Combine like terms: 0 + -7 = -7 -1w = -7 Divide each side by '-1'. w = 7 Simplifying w = 7Subproblem 2
Set the factor '(5 + 3w)' equal to zero and attempt to solve: Simplifying 5 + 3w = 0 Solving 5 + 3w = 0 Move all terms containing w to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + 3w = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 3w = 0 + -5 3w = 0 + -5 Combine like terms: 0 + -5 = -5 3w = -5 Divide each side by '3'. w = -1.666666667 Simplifying w = -1.666666667Solution
w = {7, -1.666666667}
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