(5y+2)(9-y)=0

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Solution for (5y+2)(9-y)=0 equation: 


Simplifying
(5y + 2)(9 + -1y) = 0

Reorder the terms:
(2 + 5y)(9 + -1y) = 0

Multiply (2 + 5y) * (9 + -1y)
(2(9 + -1y) + 5y * (9 + -1y)) = 0
((9 * 2 + -1y * 2) + 5y * (9 + -1y)) = 0
((18 + -2y) + 5y * (9 + -1y)) = 0
(18 + -2y + (9 * 5y + -1y * 5y)) = 0
(18 + -2y + (45y + -5y2)) = 0

Combine like terms: -2y + 45y = 43y
(18 + 43y + -5y2) = 0

Solving
18 + 43y + -5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(9 + -1y)(2 + 5y) = 0


Subproblem 1
Set the factor '(9 + -1y)' equal to zero and attempt to solve:

Simplifying
9 + -1y = 0

Solving
9 + -1y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1y = 0 + -9

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

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

Divide each side by '-1'.
y = 9

Simplifying
y = 9

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 = {9, -0.4}

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