y^2+8y+10=3

Solution for y^2+8y+10=3 equation:

Simplifying
y2 + 8y + 10 = 3

Reorder the terms:
10 + 8y + y2 = 3

Solving
10 + 8y + y2 = 3

Solving for variable 'y'.

Reorder the terms:
10 + -3 + 8y + y2 = 3 + -3

Combine like terms: 10 + -3 = 7
7 + 8y + y2 = 3 + -3

Combine like terms: 3 + -3 = 0
7 + 8y + y2 = 0

Factor a trinomial.
(7 + y)(1 + y) = 0

Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7
Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

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

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

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

Simplifying
y = -1
Solution
y = {-7, -1}