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

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


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

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

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

Combine like terms: 5v + -9v = -4v
(-45 + -4v + v2) = 0

Solving
-45 + -4v + v2 = 0

Solving for variable 'v'.

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

Subproblem 1

Set the factor '(-5 + -1v)' equal to zero and attempt to solve: Simplifying -5 + -1v = 0 Solving -5 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1v = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1v = 0 + 5 -1v = 0 + 5 Combine like terms: 0 + 5 = 5 -1v = 5 Divide each side by '-1'. v = -5 Simplifying v = -5

Subproblem 2

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

Solution

v = {-5, 9}

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