y(y-7)=-12

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

Simplifying
y(y + -7) = -12

Reorder the terms:
y(-7 + y) = -12
(-7 * y + y * y) = -12
(-7y + y2) = -12

Solving
-7y + y2 = -12

Solving for variable 'y'.

Reorder the terms:
12 + -7y + y2 = -12 + 12

Combine like terms: -12 + 12 = 0
12 + -7y + y2 = 0

Factor a trinomial.
(3 + -1y)(4 + -1y) = 0

Subproblem 1
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {3, 4}