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Simplifying (19 + -1y) * y = 84 Reorder the terms for easier multiplication: y(19 + -1y) = 84 (19 * y + -1y * y) = 84 (19y + -1y2) = 84 Solving 19y + -1y2 = 84 Solving for variable 'y'. Reorder the terms: -84 + 19y + -1y2 = 84 + -84 Combine like terms: 84 + -84 = 0 -84 + 19y + -1y2 = 0 Factor a trinomial. (-12 + y)(7 + -1y) = 0Subproblem 1
Set the factor '(-12 + y)' equal to zero and attempt to solve: Simplifying -12 + y = 0 Solving -12 + y = 0 Move all terms containing y to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + y = 0 + 12 Combine like terms: -12 + 12 = 0 0 + y = 0 + 12 y = 0 + 12 Combine like terms: 0 + 12 = 12 y = 12 Simplifying y = 12Subproblem 2
Set the factor '(7 + -1y)' equal to zero and attempt to solve: Simplifying 7 + -1y = 0 Solving 7 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1y = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1y = 0 + -7 -1y = 0 + -7 Combine like terms: 0 + -7 = -7 -1y = -7 Divide each side by '-1'. y = 7 Simplifying y = 7Solution
y = {12, 7}
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