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Simplifying (1 + w)(4w + -7) = 0 Reorder the terms: (1 + w)(-7 + 4w) = 0 Multiply (1 + w) * (-7 + 4w) (1(-7 + 4w) + w(-7 + 4w)) = 0 ((-7 * 1 + 4w * 1) + w(-7 + 4w)) = 0 ((-7 + 4w) + w(-7 + 4w)) = 0 (-7 + 4w + (-7 * w + 4w * w)) = 0 (-7 + 4w + (-7w + 4w2)) = 0 Combine like terms: 4w + -7w = -3w (-7 + -3w + 4w2) = 0 Solving -7 + -3w + 4w2 = 0 Solving for variable 'w'. Factor a trinomial. (-1 + -1w)(7 + -4w) = 0Subproblem 1
Set the factor '(-1 + -1w)' equal to zero and attempt to solve: Simplifying -1 + -1w = 0 Solving -1 + -1w = 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 + -1w = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1w = 0 + 1 -1w = 0 + 1 Combine like terms: 0 + 1 = 1 -1w = 1 Divide each side by '-1'. w = -1 Simplifying w = -1Subproblem 2
Set the factor '(7 + -4w)' equal to zero and attempt to solve: Simplifying 7 + -4w = 0 Solving 7 + -4w = 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 + -4w = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4w = 0 + -7 -4w = 0 + -7 Combine like terms: 0 + -7 = -7 -4w = -7 Divide each side by '-4'. w = 1.75 Simplifying w = 1.75Solution
w = {-1, 1.75}
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