2y(y+3)+5(y-3)=36

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Solution for 2y(y+3)+5(y-3)=36 equation: 


Simplifying
2y(y + 3) + 5(y + -3) = 36

Reorder the terms:
2y(3 + y) + 5(y + -3) = 36
(3 * 2y + y * 2y) + 5(y + -3) = 36
(6y + 2y2) + 5(y + -3) = 36

Reorder the terms:
6y + 2y2 + 5(-3 + y) = 36
6y + 2y2 + (-3 * 5 + y * 5) = 36
6y + 2y2 + (-15 + 5y) = 36

Reorder the terms:
-15 + 6y + 5y + 2y2 = 36

Combine like terms: 6y + 5y = 11y
-15 + 11y + 2y2 = 36

Solving
-15 + 11y + 2y2 = 36

Solving for variable 'y'.

Reorder the terms:
-15 + -36 + 11y + 2y2 = 36 + -36

Combine like terms: -15 + -36 = -51
-51 + 11y + 2y2 = 36 + -36

Combine like terms: 36 + -36 = 0
-51 + 11y + 2y2 = 0

Factor a trinomial.
(-17 + -2y)(3 + -1y) = 0


Subproblem 1
Set the factor '(-17 + -2y)' equal to zero and attempt to solve:

Simplifying
-17 + -2y = 0

Solving
-17 + -2y = 0

Move all terms containing y to the left, all other terms to the right.

Add '17' to each side of the equation.
-17 + 17 + -2y = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -2y = 0 + 17
-2y = 0 + 17

Combine like terms: 0 + 17 = 17
-2y = 17

Divide each side by '-2'.
y = -8.5

Simplifying
y = -8.5

Subproblem 2
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
Solution
y = {-8.5, 3}

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