2y^2+2y=1300

Solution for 2y^2+2y=1300 equation:

Simplifying
2y2 + 2y = 1300

Reorder the terms:
2y + 2y2 = 1300

Solving
2y + 2y2 = 1300

Solving for variable 'y'.

Reorder the terms:
-1300 + 2y + 2y2 = 1300 + -1300

Combine like terms: 1300 + -1300 = 0
-1300 + 2y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-650 + y + y2) = 0

Factor a trinomial.
2((-26 + -1y)(25 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-26 + -1y)' equal to zero and attempt to solve:

Simplifying
-26 + -1y = 0

Solving
-26 + -1y = 0

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

Add '26' to each side of the equation.
-26 + 26 + -1y = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -1y = 0 + 26
-1y = 0 + 26

Combine like terms: 0 + 26 = 26
-1y = 26

Divide each side by '-1'.
y = -26

Simplifying
y = -26
Subproblem 2
Set the factor '(25 + -1y)' equal to zero and attempt to solve:

Simplifying
25 + -1y = 0

Solving
25 + -1y = 0

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

Add '-25' to each side of the equation.
25 + -25 + -1y = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1y = 0 + -25
-1y = 0 + -25

Combine like terms: 0 + -25 = -25
-1y = -25

Divide each side by '-1'.
y = 25

Simplifying
y = 25
Solution
y = {-26, 25}