y^2-30y-75=100

Solution for y^2-30y-75=100 equation:

Simplifying
y2 + -30y + -75 = 100

Reorder the terms:
-75 + -30y + y2 = 100

Solving
-75 + -30y + y2 = 100

Solving for variable 'y'.

Reorder the terms:
-75 + -100 + -30y + y2 = 100 + -100

Combine like terms: -75 + -100 = -175
-175 + -30y + y2 = 100 + -100

Combine like terms: 100 + -100 = 0
-175 + -30y + y2 = 0

Factor a trinomial.
(-5 + -1y)(35 + -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 '(35 + -1y)' equal to zero and attempt to solve:

Simplifying
35 + -1y = 0

Solving
35 + -1y = 0

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

Add '-35' to each side of the equation.
35 + -35 + -1y = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -1y = 0 + -35
-1y = 0 + -35

Combine like terms: 0 + -35 = -35
-1y = -35

Divide each side by '-1'.
y = 35

Simplifying
y = 35
Solution
y = {-5, 35}