(y-2)(y-5)=28

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Solution for (y-2)(y-5)=28 equation: 


Simplifying
(y + -2)(y + -5) = 28

Reorder the terms:
(-2 + y)(y + -5) = 28

Reorder the terms:
(-2 + y)(-5 + y) = 28

Multiply (-2 + y) * (-5 + y)
(-2(-5 + y) + y(-5 + y)) = 28
((-5 * -2 + y * -2) + y(-5 + y)) = 28
((10 + -2y) + y(-5 + y)) = 28
(10 + -2y + (-5 * y + y * y)) = 28
(10 + -2y + (-5y + y2)) = 28

Combine like terms: -2y + -5y = -7y
(10 + -7y + y2) = 28

Solving
10 + -7y + y2 = 28

Solving for variable 'y'.

Reorder the terms:
10 + -28 + -7y + y2 = 28 + -28

Combine like terms: 10 + -28 = -18
-18 + -7y + y2 = 28 + -28

Combine like terms: 28 + -28 = 0
-18 + -7y + y2 = 0

Factor a trinomial.
(-2 + -1y)(9 + -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 '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1y = 0 + -9
-1y = 0 + -9

Combine like terms: 0 + -9 = -9
-1y = -9

Divide each side by '-1'.
y = 9

Simplifying
y = 9
Solution
y = {-2, 9}

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