y^2+2y-9=-3y-3

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Solution for y^2+2y-9=-3y-3 equation:


Simplifying
y2 + 2y + -9 = -3y + -3

Reorder the terms:
-9 + 2y + y2 = -3y + -3

Reorder the terms:
-9 + 2y + y2 = -3 + -3y

Solving
-9 + 2y + y2 = -3 + -3y

Solving for variable 'y'.

Reorder the terms:
-9 + 3 + 2y + 3y + y2 = -3 + -3y + 3 + 3y

Combine like terms: -9 + 3 = -6
-6 + 2y + 3y + y2 = -3 + -3y + 3 + 3y

Combine like terms: 2y + 3y = 5y
-6 + 5y + y2 = -3 + -3y + 3 + 3y

Reorder the terms:
-6 + 5y + y2 = -3 + 3 + -3y + 3y

Combine like terms: -3 + 3 = 0
-6 + 5y + y2 = 0 + -3y + 3y
-6 + 5y + y2 = -3y + 3y

Combine like terms: -3y + 3y = 0
-6 + 5y + y2 = 0

Factor a trinomial.
(-6 + -1y)(1 + -1y) = 0

Subproblem 1

Set the factor '(-6 + -1y)' equal to zero and attempt to solve: Simplifying -6 + -1y = 0 Solving -6 + -1y = 0 Move all terms containing y to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1y = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1y = 0 + 6 -1y = 0 + 6 Combine like terms: 0 + 6 = 6 -1y = 6 Divide each side by '-1'. y = -6 Simplifying y = -6

Subproblem 2

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 = 1

Solution

y = {-6, 1}

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