(4v+6)(9-v)=0

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Solution for (4v+6)(9-v)=0 equation:


Simplifying
(4v + 6)(9 + -1v) = 0

Reorder the terms:
(6 + 4v)(9 + -1v) = 0

Multiply (6 + 4v) * (9 + -1v)
(6(9 + -1v) + 4v * (9 + -1v)) = 0
((9 * 6 + -1v * 6) + 4v * (9 + -1v)) = 0
((54 + -6v) + 4v * (9 + -1v)) = 0
(54 + -6v + (9 * 4v + -1v * 4v)) = 0
(54 + -6v + (36v + -4v2)) = 0

Combine like terms: -6v + 36v = 30v
(54 + 30v + -4v2) = 0

Solving
54 + 30v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(27 + 15v + -2v2) = 0

Factor a trinomial.
2((9 + -1v)(3 + 2v)) = 0

Ignore the factor 2.

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 '(3 + 2v)' equal to zero and attempt to solve: Simplifying 3 + 2v = 0 Solving 3 + 2v = 0 Move all terms containing v to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + 2v = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 2v = 0 + -3 2v = 0 + -3 Combine like terms: 0 + -3 = -3 2v = -3 Divide each side by '2'. v = -1.5 Simplifying v = -1.5

Solution

v = {9, -1.5}

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