5y^2-6y+22=30

Solution for 5y^2-6y+22=30 equation:

Simplifying
5y2 + -6y + 22 = 30

Reorder the terms:
22 + -6y + 5y2 = 30

Solving
22 + -6y + 5y2 = 30

Solving for variable 'y'.

Reorder the terms:
22 + -30 + -6y + 5y2 = 30 + -30

Combine like terms: 22 + -30 = -8
-8 + -6y + 5y2 = 30 + -30

Combine like terms: 30 + -30 = 0
-8 + -6y + 5y2 = 0

Factor a trinomial.
(-4 + -5y)(2 + -1y) = 0

Subproblem 1
Set the factor '(-4 + -5y)' equal to zero and attempt to solve:

Simplifying
-4 + -5y = 0

Solving
-4 + -5y = 0

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

Add '4' to each side of the equation.
-4 + 4 + -5y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -5y = 0 + 4
-5y = 0 + 4

Combine like terms: 0 + 4 = 4
-5y = 4

Divide each side by '-5'.
y = -0.8

Simplifying
y = -0.8
Subproblem 2
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
Solution
y = {-0.8, 2}