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Simplifying 0 = y2 + -4y + -21 Reorder the terms: 0 = -21 + -4y + y2 Solving 0 = -21 + -4y + y2 Solving for variable 'y'. Combine like terms: 0 + 21 = 21 21 + 4y + -1y2 = -21 + -4y + y2 + 21 + 4y + -1y2 Reorder the terms: 21 + 4y + -1y2 = -21 + 21 + -4y + 4y + y2 + -1y2 Combine like terms: -21 + 21 = 0 21 + 4y + -1y2 = 0 + -4y + 4y + y2 + -1y2 21 + 4y + -1y2 = -4y + 4y + y2 + -1y2 Combine like terms: -4y + 4y = 0 21 + 4y + -1y2 = 0 + y2 + -1y2 21 + 4y + -1y2 = y2 + -1y2 Combine like terms: y2 + -1y2 = 0 21 + 4y + -1y2 = 0 Factor a trinomial. (7 + -1y)(3 + 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 '(3 + y)' equal to zero and attempt to solve: Simplifying 3 + y = 0 Solving 3 + y = 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 + y = 0 + -3 Combine like terms: 3 + -3 = 0 0 + y = 0 + -3 y = 0 + -3 Combine like terms: 0 + -3 = -3 y = -3 Simplifying y = -3Solution
y = {7, -3}
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