2y(y+4)=10

Solution for 2y(y+4)=10 equation:

Simplifying
2y(y + 4) = 10

Reorder the terms:
2y(4 + y) = 10
(4 * 2y + y * 2y) = 10
(8y + 2y2) = 10

Solving
8y + 2y2 = 10

Solving for variable 'y'.

Reorder the terms:
-10 + 8y + 2y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 8y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 4y + y2) = 0

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

Ignore the factor 2.
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 '(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 = {-5, 1}