y(y-7)=30

Solution for y(y-7)=30 equation:

Simplifying
y(y + -7) = 30

Reorder the terms:
y(-7 + y) = 30
(-7 * y + y * y) = 30
(-7y + y2) = 30

Solving
-7y + y2 = 30

Solving for variable 'y'.

Reorder the terms:
-30 + -7y + y2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -7y + y2 = 0

Factor a trinomial.
(-3 + -1y)(10 + -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 '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10
Solution
y = {-3, 10}