5y(y-5)+(y-5)=

Solution for 5y(y-5)+(y-5)= equation:

Simplifying
5y(y + -5) + (y + -5) = 0

Reorder the terms:
5y(-5 + y) + (y + -5) = 0
(-5 * 5y + y * 5y) + (y + -5) = 0
(-25y + 5y2) + (y + -5) = 0

Reorder the terms:
-25y + 5y2 + (-5 + y) = 0

Remove parenthesis around (-5 + y)
-25y + 5y2 + -5 + y = 0

Reorder the terms:
-5 + -25y + y + 5y2 = 0

Combine like terms: -25y + y = -24y
-5 + -24y + 5y2 = 0

Solving
-5 + -24y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-1 + -5y)(5 + -1y) = 0

Subproblem 1
Set the factor '(-1 + -5y)' equal to zero and attempt to solve:

Simplifying
-1 + -5y = 0

Solving
-1 + -5y = 0

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

Add '1' to each side of the equation.
-1 + 1 + -5y = 0 + 1

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

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

Divide each side by '-5'.
y = -0.2

Simplifying
y = -0.2
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 = {-0.2, 5}