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Simplifying (5y + -3)(7 + y) = 0 Reorder the terms: (-3 + 5y)(7 + y) = 0 Multiply (-3 + 5y) * (7 + y) (-3(7 + y) + 5y * (7 + y)) = 0 ((7 * -3 + y * -3) + 5y * (7 + y)) = 0 ((-21 + -3y) + 5y * (7 + y)) = 0 (-21 + -3y + (7 * 5y + y * 5y)) = 0 (-21 + -3y + (35y + 5y2)) = 0 Combine like terms: -3y + 35y = 32y (-21 + 32y + 5y2) = 0 Solving -21 + 32y + 5y2 = 0 Solving for variable 'y'. Factor a trinomial. (-7 + -1y)(3 + -5y) = 0Subproblem 1
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 = -7Subproblem 2
Set the factor '(3 + -5y)' equal to zero and attempt to solve: Simplifying 3 + -5y = 0 Solving 3 + -5y = 0 Move all terms containing y to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5y = 0 + -3 -5y = 0 + -3 Combine like terms: 0 + -3 = -3 -5y = -3 Divide each side by '-5'. y = 0.6 Simplifying y = 0.6Solution
y = {-7, 0.6}
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