5y^2=8y-3

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

Simplifying
5y2 = 8y + -3

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

Solving
5y2 = -3 + 8y

Solving for variable 'y'.

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

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

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

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

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

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

Simplifying
1 + -1y = 0

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

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

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

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

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