(y-12)(y+7)=0

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Solution for (y-12)(y+7)=0 equation: 


Simplifying
(y + -12)(y + 7) = 0

Reorder the terms:
(-12 + y)(y + 7) = 0

Reorder the terms:
(-12 + y)(7 + y) = 0

Multiply (-12 + y) * (7 + y)
(-12(7 + y) + y(7 + y)) = 0
((7 * -12 + y * -12) + y(7 + y)) = 0
((-84 + -12y) + y(7 + y)) = 0
(-84 + -12y + (7 * y + y * y)) = 0
(-84 + -12y + (7y + y2)) = 0

Combine like terms: -12y + 7y = -5y
(-84 + -5y + y2) = 0

Solving
-84 + -5y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-7 + -1y)(12 + -1y) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(12 + -1y)' equal to zero and attempt to solve:

Simplifying
12 + -1y = 0

Solving
12 + -1y = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1y = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1y = 0 + -12
-1y = 0 + -12

Combine like terms: 0 + -12 = -12
-1y = -12

Divide each side by '-1'.
y = 12

Simplifying
y = 12
Solution
y = {-7, 12}

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