5y(y-1)-2(2y^2-7y)=-8

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Solution for 5y(y-1)-2(2y^2-7y)=-8 equation: 


Simplifying
5y(y + -1) + -2(2y2 + -7y) = -8

Reorder the terms:
5y(-1 + y) + -2(2y2 + -7y) = -8
(-1 * 5y + y * 5y) + -2(2y2 + -7y) = -8
(-5y + 5y2) + -2(2y2 + -7y) = -8

Reorder the terms:
-5y + 5y2 + -2(-7y + 2y2) = -8
-5y + 5y2 + (-7y * -2 + 2y2 * -2) = -8
-5y + 5y2 + (14y + -4y2) = -8

Reorder the terms:
-5y + 14y + 5y2 + -4y2 = -8

Combine like terms: -5y + 14y = 9y
9y + 5y2 + -4y2 = -8

Combine like terms: 5y2 + -4y2 = 1y2
9y + 1y2 = -8

Solving
9y + 1y2 = -8

Solving for variable 'y'.

Reorder the terms:
8 + 9y + 1y2 = -8 + 8

Combine like terms: -8 + 8 = 0
8 + 9y + 1y2 = 0

Factor a trinomial.
(8 + y)(1 + y) = 0


Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8

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 = {-8, -1}

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