(y-3)(5y-10)=0

Solution for (y-3)(5y-10)=0 equation:

Simplifying
(y + -3)(5y + -10) = 0

Reorder the terms:
(-3 + y)(5y + -10) = 0

Reorder the terms:
(-3 + y)(-10 + 5y) = 0

Multiply (-3 + y) * (-10 + 5y)
(-3(-10 + 5y) + y(-10 + 5y)) = 0
((-10 * -3 + 5y * -3) + y(-10 + 5y)) = 0
((30 + -15y) + y(-10 + 5y)) = 0
(30 + -15y + (-10 * y + 5y * y)) = 0
(30 + -15y + (-10y + 5y2)) = 0

Combine like terms: -15y + -10y = -25y
(30 + -25y + 5y2) = 0

Solving
30 + -25y + 5y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(6 + -5y + y2) = 0

Factor a trinomial.
5((2 + -1y)(3 + -1y)) = 0

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

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {2, 3}