4y^2+4y+1+y^2=13

Solution for 4y^2+4y+1+y^2=13 equation:

Simplifying
4y2 + 4y + 1 + y2 = 13

Reorder the terms:
1 + 4y + 4y2 + y2 = 13

Combine like terms: 4y2 + y2 = 5y2
1 + 4y + 5y2 = 13

Solving
1 + 4y + 5y2 = 13

Solving for variable 'y'.

Reorder the terms:
1 + -13 + 4y + 5y2 = 13 + -13

Combine like terms: 1 + -13 = -12
-12 + 4y + 5y2 = 13 + -13

Combine like terms: 13 + -13 = 0
-12 + 4y + 5y2 = 0

Factor a trinomial.
(-2 + -1y)(6 + -5y) = 0

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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
y = -2

Simplifying
y = -2
Subproblem 2
Set the factor '(6 + -5y)' equal to zero and attempt to solve:

Simplifying
6 + -5y = 0

Solving
6 + -5y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5y = 0 + -6
-5y = 0 + -6

Combine like terms: 0 + -6 = -6
-5y = -6

Divide each side by '-5'.
y = 1.2

Simplifying
y = 1.2
Solution
y = {-2, 1.2}