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

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


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

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

Multiply (-2 + 5y) * (5 + y)
(-2(5 + y) + 5y * (5 + y)) = 0
((5 * -2 + y * -2) + 5y * (5 + y)) = 0
((-10 + -2y) + 5y * (5 + y)) = 0
(-10 + -2y + (5 * 5y + y * 5y)) = 0
(-10 + -2y + (25y + 5y2)) = 0

Combine like terms: -2y + 25y = 23y
(-10 + 23y + 5y2) = 0

Solving
-10 + 23y + 5y2 = 0

Solving for variable 'y'.

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


Subproblem 1
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

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

Simplifying
2 + -5y = 0

Solving
2 + -5y = 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 + -5y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5y = 0 + -2
-5y = 0 + -2

Combine like terms: 0 + -2 = -2
-5y = -2

Divide each side by '-5'.
y = 0.4

Simplifying
y = 0.4
Solution
y = {-5, 0.4}

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