=5y^2+8y+3

Solution for =5y^2+8y+3 equation:

Simplifying
0 = 5y2 + 8y + 3

Reorder the terms:
0 = 3 + 8y + 5y2

Solving
0 = 3 + 8y + 5y2

Solving for variable 'y'.

Combine like terms: 0 + -3 = -3
-3 + -8y + -5y2 = 3 + 8y + 5y2 + -3 + -8y + -5y2

Reorder the terms:
-3 + -8y + -5y2 = 3 + -3 + 8y + -8y + 5y2 + -5y2

Combine like terms: 3 + -3 = 0
-3 + -8y + -5y2 = 0 + 8y + -8y + 5y2 + -5y2
-3 + -8y + -5y2 = 8y + -8y + 5y2 + -5y2

Combine like terms: 8y + -8y = 0
-3 + -8y + -5y2 = 0 + 5y2 + -5y2
-3 + -8y + -5y2 = 5y2 + -5y2

Combine like terms: 5y2 + -5y2 = 0
-3 + -8y + -5y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 8y + 5y2) = 0

Factor a trinomial.
-1((1 + y)(3 + 5y)) = 0

Ignore the factor -1.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + 5y)' equal to zero and attempt to solve:

Simplifying
3 + 5y = 0

Solving
3 + 5y = 0

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

Add '-3' to each side of the equation.
3 + -3 + 5y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 5y = 0 + -3
5y = 0 + -3

Combine like terms: 0 + -3 = -3
5y = -3

Divide each side by '5'.
y = -0.6

Simplifying
y = -0.6
Solution
y = {-1, -0.6}