y(y-3)=40

Solution for y(y-3)=40 equation:

Simplifying
y(y + -3) = 40

Reorder the terms:
y(-3 + y) = 40
(-3 * y + y * y) = 40
(-3y + y2) = 40

Solving
-3y + y2 = 40

Solving for variable 'y'.

Reorder the terms:
-40 + -3y + y2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + -3y + y2 = 0

Factor a trinomial.
(-5 + -1y)(8 + -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 '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

Simplifying
y = 8
Solution
y = {-5, 8}