y(y-13)=48

Solution for y(y-13)=48 equation:

Simplifying
y(y + -13) = 48

Reorder the terms:
y(-13 + y) = 48
(-13 * y + y * y) = 48
(-13y + y2) = 48

Solving
-13y + y2 = 48

Solving for variable 'y'.

Reorder the terms:
-48 + -13y + y2 = 48 + -48

Combine like terms: 48 + -48 = 0
-48 + -13y + y2 = 0

Factor a trinomial.
(-3 + -1y)(16 + -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 '(16 + -1y)' equal to zero and attempt to solve:

Simplifying
16 + -1y = 0

Solving
16 + -1y = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1y = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1y = 0 + -16
-1y = 0 + -16

Combine like terms: 0 + -16 = -16
-1y = -16

Divide each side by '-1'.
y = 16

Simplifying
y = 16
Solution
y = {-3, 16}