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Simplifying 6y + 10 = y2 + 3 Reorder the terms: 10 + 6y = y2 + 3 Reorder the terms: 10 + 6y = 3 + y2 Solving 10 + 6y = 3 + y2 Solving for variable 'y'. Reorder the terms: 10 + -3 + 6y + -1y2 = 3 + y2 + -3 + -1y2 Combine like terms: 10 + -3 = 7 7 + 6y + -1y2 = 3 + y2 + -3 + -1y2 Reorder the terms: 7 + 6y + -1y2 = 3 + -3 + y2 + -1y2 Combine like terms: 3 + -3 = 0 7 + 6y + -1y2 = 0 + y2 + -1y2 7 + 6y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 7 + 6y + -1y2 = 0 Factor a trinomial. (7 + -1y)(1 + y) = 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 '(1 + y)' equal to zero and attempt to solve: Simplifying 1 + y = 0 Solving 1 + y = 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 + y = 0 + -1 Combine like terms: 1 + -1 = 0 0 + y = 0 + -1 y = 0 + -1 Combine like terms: 0 + -1 = -1 y = -1 Simplifying y = -1Solution
y = {7, -1}
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