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.
(-35 + -1y)(5 + -1y) = 0

Subproblem 1
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
Subproblem 2
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
Solution
y = {-35, 5}