2(2y-1)(y+5)+y(y+5)=0

Solution for 2(2y-1)(y+5)+y(y+5)=0 equation:

Simplifying
2(2y + -1)(y + 5) + y(y + 5) = 0

Reorder the terms:
2(-1 + 2y)(y + 5) + y(y + 5) = 0

Reorder the terms:
2(-1 + 2y)(5 + y) + y(y + 5) = 0

Multiply (-1 + 2y) * (5 + y)
2(-1(5 + y) + 2y * (5 + y)) + y(y + 5) = 0
2((5 * -1 + y * -1) + 2y * (5 + y)) + y(y + 5) = 0
2((-5 + -1y) + 2y * (5 + y)) + y(y + 5) = 0
2(-5 + -1y + (5 * 2y + y * 2y)) + y(y + 5) = 0
2(-5 + -1y + (10y + 2y2)) + y(y + 5) = 0

Combine like terms: -1y + 10y = 9y
2(-5 + 9y + 2y2) + y(y + 5) = 0
(-5 * 2 + 9y * 2 + 2y2 * 2) + y(y + 5) = 0
(-10 + 18y + 4y2) + y(y + 5) = 0

Reorder the terms:
-10 + 18y + 4y2 + y(5 + y) = 0
-10 + 18y + 4y2 + (5 * y + y * y) = 0
-10 + 18y + 4y2 + (5y + y2) = 0

Reorder the terms:
-10 + 18y + 5y + 4y2 + y2 = 0

Combine like terms: 18y + 5y = 23y
-10 + 23y + 4y2 + y2 = 0

Combine like terms: 4y2 + y2 = 5y2
-10 + 23y + 5y2 = 0

Solving
-10 + 23y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-5 + -1y)(2 + -5y) = 0

Subproblem 1
Set the factor '(-5 + -1y)' equal to zero and attempt to solve:

Simplifying
-5 + -1y = 0

Solving
-5 + -1y = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1y = 0 + 5
-1y = 0 + 5

Combine like terms: 0 + 5 = 5
-1y = 5

Divide each side by '-1'.
y = -5

Simplifying
y = -5
Subproblem 2
Set the factor '(2 + -5y)' equal to zero and attempt to solve:

Simplifying
2 + -5y = 0

Solving
2 + -5y = 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 + -5y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5y = 0 + -2
-5y = 0 + -2

Combine like terms: 0 + -2 = -2
-5y = -2

Divide each side by '-5'.
y = 0.4

Simplifying
y = 0.4
Solution
y = {-5, 0.4}