(8Y^2-18Y+10)=0

Solution for (8Y^2-18Y+10)=0 equation:

Simplifying
(8Y2 + -18Y + 10) = 0

Reorder the terms:
(10 + -18Y + 8Y2) = 0

Remove parenthesis around (10 + -18Y + 8Y2)
10 + -18Y + 8Y2 = 0

Solving
10 + -18Y + 8Y2 = 0

Solving for variable 'Y'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -9Y + 4Y2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -4Y)' equal to zero and attempt to solve:

Simplifying
5 + -4Y = 0

Solving
5 + -4Y = 0

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

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

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

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

Divide each side by '-4'.
Y = 1.25

Simplifying
Y = 1.25
Solution
Y = {1, 1.25}