-5y(y-2)=8-4y

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Solution for -5y(y-2)=8-4y equation: 


Simplifying
-5y(y + -2) = 8 + -4y

Reorder the terms:
-5y(-2 + y) = 8 + -4y
(-2 * -5y + y * -5y) = 8 + -4y
(10y + -5y2) = 8 + -4y

Solving
10y + -5y2 = 8 + -4y

Solving for variable 'y'.

Reorder the terms:
-8 + 10y + 4y + -5y2 = 8 + -4y + -8 + 4y

Combine like terms: 10y + 4y = 14y
-8 + 14y + -5y2 = 8 + -4y + -8 + 4y

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

Combine like terms: 8 + -8 = 0
-8 + 14y + -5y2 = 0 + -4y + 4y
-8 + 14y + -5y2 = -4y + 4y

Combine like terms: -4y + 4y = 0
-8 + 14y + -5y2 = 0

Factor a trinomial.
(-2 + y)(4 + -5y) = 0


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

Simplifying
-2 + y = 0

Solving
-2 + y = 0

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

Add '2' to each side of the equation.
-2 + 2 + y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + y = 0 + 2
y = 0 + 2

Combine like terms: 0 + 2 = 2
y = 2

Simplifying
y = 2

Subproblem 2
Set the factor '(4 + -5y)' equal to zero and attempt to solve:

Simplifying
4 + -5y = 0

Solving
4 + -5y = 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 + -5y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5y = 0 + -4
-5y = 0 + -4

Combine like terms: 0 + -4 = -4
-5y = -4

Divide each side by '-5'.
y = 0.8

Simplifying
y = 0.8
Solution
y = {2, 0.8}

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