(5y-4)(2+y)=0

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Solution for (5y-4)(2+y)=0 equation: 


Simplifying
(5y + -4)(2 + y) = 0

Reorder the terms:
(-4 + 5y)(2 + y) = 0

Multiply (-4 + 5y) * (2 + y)
(-4(2 + y) + 5y * (2 + y)) = 0
((2 * -4 + y * -4) + 5y * (2 + y)) = 0
((-8 + -4y) + 5y * (2 + y)) = 0
(-8 + -4y + (2 * 5y + y * 5y)) = 0
(-8 + -4y + (10y + 5y2)) = 0

Combine like terms: -4y + 10y = 6y
(-8 + 6y + 5y2) = 0

Solving
-8 + 6y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-2 + -1y)(4 + -5y) = 0


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

Simplifying
-2 + -1y = 0

Solving
-2 + -1y = 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 + -1y = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1y = 0 + 2
-1y = 0 + 2

Combine like terms: 0 + 2 = 2
-1y = 2

Divide each side by '-1'.
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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