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

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


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

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

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

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

Combine like terms: -9v + 2v = -7v
(-18 + -7v + v2) = 0

Solving
-18 + -7v + v2 = 0

Solving for variable 'v'.

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

Subproblem 1

Set the factor '(-2 + -1v)' equal to zero and attempt to solve: Simplifying -2 + -1v = 0 Solving -2 + -1v = 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 + -1v = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1v = 0 + 2 -1v = 0 + 2 Combine like terms: 0 + 2 = 2 -1v = 2 Divide each side by '-1'. v = -2 Simplifying v = -2

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 = {-2, 9}

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