-15y(y+1)+50(y+1)=-10y-10

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Solution for -15y(y+1)+50(y+1)=-10y-10 equation: 


Simplifying
-15y(y + 1) + 50(y + 1) = -10y + -10

Reorder the terms:
-15y(1 + y) + 50(y + 1) = -10y + -10
(1 * -15y + y * -15y) + 50(y + 1) = -10y + -10
(-15y + -15y2) + 50(y + 1) = -10y + -10

Reorder the terms:
-15y + -15y2 + 50(1 + y) = -10y + -10
-15y + -15y2 + (1 * 50 + y * 50) = -10y + -10
-15y + -15y2 + (50 + 50y) = -10y + -10

Reorder the terms:
50 + -15y + 50y + -15y2 = -10y + -10

Combine like terms: -15y + 50y = 35y
50 + 35y + -15y2 = -10y + -10

Reorder the terms:
50 + 35y + -15y2 = -10 + -10y

Solving
50 + 35y + -15y2 = -10 + -10y

Solving for variable 'y'.

Reorder the terms:
50 + 10 + 35y + 10y + -15y2 = -10 + -10y + 10 + 10y

Combine like terms: 50 + 10 = 60
60 + 35y + 10y + -15y2 = -10 + -10y + 10 + 10y

Combine like terms: 35y + 10y = 45y
60 + 45y + -15y2 = -10 + -10y + 10 + 10y

Reorder the terms:
60 + 45y + -15y2 = -10 + 10 + -10y + 10y

Combine like terms: -10 + 10 = 0
60 + 45y + -15y2 = 0 + -10y + 10y
60 + 45y + -15y2 = -10y + 10y

Combine like terms: -10y + 10y = 0
60 + 45y + -15y2 = 0

Factor out the Greatest Common Factor (GCF), '15'.
15(4 + 3y + -1y2) = 0

Factor a trinomial.
15((4 + -1y)(1 + y)) = 0

Ignore the factor 15.

Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4

Subproblem 2
Set the factor '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 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 + y = 0 + -1

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

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

Simplifying
y = -1
Solution
y = {4, -1}

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