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

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Solution for (8-v)(4v+6)=0 equation:


Simplifying
(8 + -1v)(4v + 6) = 0

Reorder the terms:
(8 + -1v)(6 + 4v) = 0

Multiply (8 + -1v) * (6 + 4v)
(8(6 + 4v) + -1v * (6 + 4v)) = 0
((6 * 8 + 4v * 8) + -1v * (6 + 4v)) = 0
((48 + 32v) + -1v * (6 + 4v)) = 0
(48 + 32v + (6 * -1v + 4v * -1v)) = 0
(48 + 32v + (-6v + -4v2)) = 0

Combine like terms: 32v + -6v = 26v
(48 + 26v + -4v2) = 0

Solving
48 + 26v + -4v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + 13v + -2v2) = 0

Factor a trinomial.
2((8 + -1v)(3 + 2v)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(8 + -1v)' equal to zero and attempt to solve: Simplifying 8 + -1v = 0 Solving 8 + -1v = 0 Move all terms containing v to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1v = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1v = 0 + -8 -1v = 0 + -8 Combine like terms: 0 + -8 = -8 -1v = -8 Divide each side by '-1'. v = 8 Simplifying v = 8

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 = {8, -1.5}

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