y^2+4y-35=5y-5

Solution for y^2+4y-35=5y-5 equation:

Simplifying
y2 + 4y + -35 = 5y + -5

Reorder the terms:
-35 + 4y + y2 = 5y + -5

Reorder the terms:
-35 + 4y + y2 = -5 + 5y

Solving
-35 + 4y + y2 = -5 + 5y

Solving for variable 'y'.

Reorder the terms:
-35 + 5 + 4y + -5y + y2 = -5 + 5y + 5 + -5y

Combine like terms: -35 + 5 = -30
-30 + 4y + -5y + y2 = -5 + 5y + 5 + -5y

Combine like terms: 4y + -5y = -1y
-30 + -1y + y2 = -5 + 5y + 5 + -5y

Reorder the terms:
-30 + -1y + y2 = -5 + 5 + 5y + -5y

Combine like terms: -5 + 5 = 0
-30 + -1y + y2 = 0 + 5y + -5y
-30 + -1y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-30 + -1y + y2 = 0

Factor a trinomial.
(-5 + -1y)(6 + -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 '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-5, 6}