(5y-2)(6-y)=0

Solution for (5y-2)(6-y)=0 equation:

Simplifying
(5y + -2)(6 + -1y) = 0

Reorder the terms:
(-2 + 5y)(6 + -1y) = 0

Multiply (-2 + 5y) * (6 + -1y)
(-2(6 + -1y) + 5y * (6 + -1y)) = 0
((6 * -2 + -1y * -2) + 5y * (6 + -1y)) = 0
((-12 + 2y) + 5y * (6 + -1y)) = 0
(-12 + 2y + (6 * 5y + -1y * 5y)) = 0
(-12 + 2y + (30y + -5y2)) = 0

Combine like terms: 2y + 30y = 32y
(-12 + 32y + -5y2) = 0

Solving
-12 + 32y + -5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-6 + y)(2 + -5y) = 0

Subproblem 1
Set the factor '(-6 + y)' equal to zero and attempt to solve:

Simplifying
-6 + y = 0

Solving
-6 + y = 0

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

Add '6' to each side of the equation.
-6 + 6 + y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + y = 0 + 6
y = 0 + 6

Combine like terms: 0 + 6 = 6
y = 6

Simplifying
y = 6
Subproblem 2
Set the factor '(2 + -5y)' equal to zero and attempt to solve:

Simplifying
2 + -5y = 0

Solving
2 + -5y = 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 + -5y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5y = 0 + -2
-5y = 0 + -2

Combine like terms: 0 + -2 = -2
-5y = -2

Divide each side by '-5'.
y = 0.4

Simplifying
y = 0.4
Solution
y = {6, 0.4}