(y-5)(y-2)-28=0

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Solution for (y-5)(y-2)-28=0 equation: 


Simplifying
(y + -5)(y + -2) + -28 = 0

Reorder the terms:
(-5 + y)(y + -2) + -28 = 0

Reorder the terms:
(-5 + y)(-2 + y) + -28 = 0

Multiply (-5 + y) * (-2 + y)
(-5(-2 + y) + y(-2 + y)) + -28 = 0
((-2 * -5 + y * -5) + y(-2 + y)) + -28 = 0
((10 + -5y) + y(-2 + y)) + -28 = 0
(10 + -5y + (-2 * y + y * y)) + -28 = 0
(10 + -5y + (-2y + y2)) + -28 = 0

Combine like terms: -5y + -2y = -7y
(10 + -7y + y2) + -28 = 0

Reorder the terms:
10 + -28 + -7y + y2 = 0

Combine like terms: 10 + -28 = -18
-18 + -7y + y2 = 0

Solving
-18 + -7y + y2 = 0

Solving for variable 'y'.

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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