15y=11-y^2+5y

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Solution for 15y=11-y^2+5y equation: 


Simplifying
15y = 11 + -1y2 + 5y

Reorder the terms:
15y = 11 + 5y + -1y2

Solving
15y = 11 + 5y + -1y2

Solving for variable 'y'.

Reorder the terms:
-11 + 15y + -5y + y2 = 11 + 5y + -1y2 + -11 + -5y + y2

Combine like terms: 15y + -5y = 10y
-11 + 10y + y2 = 11 + 5y + -1y2 + -11 + -5y + y2

Reorder the terms:
-11 + 10y + y2 = 11 + -11 + 5y + -5y + -1y2 + y2

Combine like terms: 11 + -11 = 0
-11 + 10y + y2 = 0 + 5y + -5y + -1y2 + y2
-11 + 10y + y2 = 5y + -5y + -1y2 + y2

Combine like terms: 5y + -5y = 0
-11 + 10y + y2 = 0 + -1y2 + y2
-11 + 10y + y2 = -1y2 + y2

Combine like terms: -1y2 + y2 = 0
-11 + 10y + y2 = 0

Factor a trinomial.
(-11 + -1y)(1 + -1y) = 0


Subproblem 1
Set the factor '(-11 + -1y)' equal to zero and attempt to solve:

Simplifying
-11 + -1y = 0

Solving
-11 + -1y = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1y = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1y = 0 + 11
-1y = 0 + 11

Combine like terms: 0 + 11 = 11
-1y = 11

Divide each side by '-1'.
y = -11

Simplifying
y = -11

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 = {-11, 1}

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