2y(y+5)=y^2+11

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Solution for 2y(y+5)=y^2+11 equation: 


Simplifying
2y(y + 5) = y2 + 11

Reorder the terms:
2y(5 + y) = y2 + 11
(5 * 2y + y * 2y) = y2 + 11
(10y + 2y2) = y2 + 11

Reorder the terms:
10y + 2y2 = 11 + y2

Solving
10y + 2y2 = 11 + y2

Solving for variable 'y'.

Reorder the terms:
-11 + 10y + 2y2 + -1y2 = 11 + y2 + -11 + -1y2

Combine like terms: 2y2 + -1y2 = 1y2
-11 + 10y + 1y2 = 11 + y2 + -11 + -1y2

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

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

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