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Simplifying 3y(y + 5) + -42 = 0 Reorder the terms: 3y(5 + y) + -42 = 0 (5 * 3y + y * 3y) + -42 = 0 (15y + 3y2) + -42 = 0 Reorder the terms: -42 + 15y + 3y2 = 0 Solving -42 + 15y + 3y2 = 0 Solving for variable 'y'. Factor out the Greatest Common Factor (GCF), '3'. 3(-14 + 5y + y2) = 0 Factor a trinomial. 3((-7 + -1y)(2 + -1y)) = 0 Ignore the factor 3.Subproblem 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 '(2 + -1y)' equal to zero and attempt to solve: Simplifying 2 + -1y = 0 Solving 2 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1y = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1y = 0 + -2 -1y = 0 + -2 Combine like terms: 0 + -2 = -2 -1y = -2 Divide each side by '-1'. y = 2 Simplifying y = 2Solution
y = {-7, 2}
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