(y+2)(y+7)=y*2+6y+20

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Solution for (y+2)(y+7)=y*2+6y+20 equation:


Simplifying
(y + 2)(y + 7) = y * 2 + 6y + 20

Reorder the terms:
(2 + y)(y + 7) = y * 2 + 6y + 20

Reorder the terms:
(2 + y)(7 + y) = y * 2 + 6y + 20

Multiply (2 + y) * (7 + y)
(2(7 + y) + y(7 + y)) = y * 2 + 6y + 20
((7 * 2 + y * 2) + y(7 + y)) = y * 2 + 6y + 20
((14 + 2y) + y(7 + y)) = y * 2 + 6y + 20
(14 + 2y + (7 * y + y * y)) = y * 2 + 6y + 20
(14 + 2y + (7y + y2)) = y * 2 + 6y + 20

Combine like terms: 2y + 7y = 9y
(14 + 9y + y2) = y * 2 + 6y + 20

Reorder the terms for easier multiplication:
14 + 9y + y2 = 2y + 6y + 20

Reorder the terms:
14 + 9y + y2 = 20 + 2y + 6y

Combine like terms: 2y + 6y = 8y
14 + 9y + y2 = 20 + 8y

Solving
14 + 9y + y2 = 20 + 8y

Solving for variable 'y'.

Reorder the terms:
14 + -20 + 9y + -8y + y2 = 20 + 8y + -20 + -8y

Combine like terms: 14 + -20 = -6
-6 + 9y + -8y + y2 = 20 + 8y + -20 + -8y

Combine like terms: 9y + -8y = 1y
-6 + 1y + y2 = 20 + 8y + -20 + -8y

Reorder the terms:
-6 + 1y + y2 = 20 + -20 + 8y + -8y

Combine like terms: 20 + -20 = 0
-6 + 1y + y2 = 0 + 8y + -8y
-6 + 1y + y2 = 8y + -8y

Combine like terms: 8y + -8y = 0
-6 + 1y + y2 = 0

Factor a trinomial.
(-3 + -1y)(2 + -1y) = 0

Subproblem 1

Set the factor '(-3 + -1y)' equal to zero and attempt to solve: Simplifying -3 + -1y = 0 Solving -3 + -1y = 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 + -1y = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1y = 0 + 3 -1y = 0 + 3 Combine like terms: 0 + 3 = 3 -1y = 3 Divide each side by '-1'. y = -3 Simplifying y = -3

Subproblem 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 = 2

Solution

y = {-3, 2}

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