y(y-12)=-35

Solution for y(y-12)=-35 equation:

Simplifying
y(y + -12) = -35

Reorder the terms:
y(-12 + y) = -35
(-12 * y + y * y) = -35
(-12y + y2) = -35

Solving
-12y + y2 = -35

Solving for variable 'y'.

Reorder the terms:
35 + -12y + y2 = -35 + 35

Combine like terms: -35 + 35 = 0
35 + -12y + y2 = 0

Factor a trinomial.
(5 + -1y)(7 + -1y) = 0

Subproblem 1
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
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 = {5, 7}