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

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


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

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

Multiply (2 + 5v) * (9 + -1v)
(2(9 + -1v) + 5v * (9 + -1v)) = 0
((9 * 2 + -1v * 2) + 5v * (9 + -1v)) = 0
((18 + -2v) + 5v * (9 + -1v)) = 0
(18 + -2v + (9 * 5v + -1v * 5v)) = 0
(18 + -2v + (45v + -5v2)) = 0

Combine like terms: -2v + 45v = 43v
(18 + 43v + -5v2) = 0

Solving
18 + 43v + -5v2 = 0

Solving for variable 'v'.

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


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

Simplifying
9 + -1v = 0

Solving
9 + -1v = 0

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

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

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

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

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

Simplifying
v = 9

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

Simplifying
2 + 5v = 0

Solving
2 + 5v = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5v = 0 + -2

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

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

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

Simplifying
v = -0.4
Solution
v = {9, -0.4}

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