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Simplifying 8y2 + 33y + 2 = 7y2 + 42y + -6 Reorder the terms: 2 + 33y + 8y2 = 7y2 + 42y + -6 Reorder the terms: 2 + 33y + 8y2 = -6 + 42y + 7y2 Solving 2 + 33y + 8y2 = -6 + 42y + 7y2 Solving for variable 'y'. Reorder the terms: 2 + 6 + 33y + -42y + 8y2 + -7y2 = -6 + 42y + 7y2 + 6 + -42y + -7y2 Combine like terms: 2 + 6 = 8 8 + 33y + -42y + 8y2 + -7y2 = -6 + 42y + 7y2 + 6 + -42y + -7y2 Combine like terms: 33y + -42y = -9y 8 + -9y + 8y2 + -7y2 = -6 + 42y + 7y2 + 6 + -42y + -7y2 Combine like terms: 8y2 + -7y2 = 1y2 8 + -9y + 1y2 = -6 + 42y + 7y2 + 6 + -42y + -7y2 Reorder the terms: 8 + -9y + 1y2 = -6 + 6 + 42y + -42y + 7y2 + -7y2 Combine like terms: -6 + 6 = 0 8 + -9y + 1y2 = 0 + 42y + -42y + 7y2 + -7y2 8 + -9y + 1y2 = 42y + -42y + 7y2 + -7y2 Combine like terms: 42y + -42y = 0 8 + -9y + 1y2 = 0 + 7y2 + -7y2 8 + -9y + 1y2 = 7y2 + -7y2 Combine like terms: 7y2 + -7y2 = 0 8 + -9y + 1y2 = 0 Factor a trinomial. (1 + -1y)(8 + -1y) = 0Subproblem 1
Set the factor '(1 + -1y)' equal to zero and attempt to solve: Simplifying 1 + -1y = 0 Solving 1 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1y = 0 + -1 -1y = 0 + -1 Combine like terms: 0 + -1 = -1 -1y = -1 Divide each side by '-1'. y = 1 Simplifying y = 1Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve: Simplifying 8 + -1y = 0 Solving 8 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1y = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1y = 0 + -8 -1y = 0 + -8 Combine like terms: 0 + -8 = -8 -1y = -8 Divide each side by '-1'. y = 8 Simplifying y = 8Solution
y = {1, 8}
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