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

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


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

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

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

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

Combine like terms: -2y + -7y = -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}

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