(y-7)(y-2)=0

Solution for (y-7)(y-2)=0 equation:

Simplifying
(y + -7)(y + -2) = 0

Reorder the terms:
(-7 + y)(y + -2) = 0

Reorder the terms:
(-7 + y)(-2 + y) = 0

Multiply (-7 + y) * (-2 + y)
(-7(-2 + y) + y(-2 + y)) = 0
((-2 * -7 + y * -7) + y(-2 + y)) = 0
((14 + -7y) + y(-2 + y)) = 0
(14 + -7y + (-2 * y + y * y)) = 0
(14 + -7y + (-2y + y2)) = 0

Combine like terms: -7y + -2y = -9y
(14 + -9y + y2) = 0

Solving
14 + -9y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(2 + -1y)(7 + -1y) = 0

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 '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {2, 7}