(5v-10)(4v+3)=0

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Solution for (5v-10)(4v+3)=0 equation:


Simplifying
(5v + -10)(4v + 3) = 0

Reorder the terms:
(-10 + 5v)(4v + 3) = 0

Reorder the terms:
(-10 + 5v)(3 + 4v) = 0

Multiply (-10 + 5v) * (3 + 4v)
(-10(3 + 4v) + 5v * (3 + 4v)) = 0
((3 * -10 + 4v * -10) + 5v * (3 + 4v)) = 0
((-30 + -40v) + 5v * (3 + 4v)) = 0
(-30 + -40v + (3 * 5v + 4v * 5v)) = 0
(-30 + -40v + (15v + 20v2)) = 0

Combine like terms: -40v + 15v = -25v
(-30 + -25v + 20v2) = 0

Solving
-30 + -25v + 20v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + -5v + 4v2) = 0

Factor a trinomial.
5((-3 + -4v)(2 + -1v)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-3 + -4v)' equal to zero and attempt to solve: Simplifying -3 + -4v = 0 Solving -3 + -4v = 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 + -4v = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -4v = 0 + 3 -4v = 0 + 3 Combine like terms: 0 + 3 = 3 -4v = 3 Divide each side by '-4'. v = -0.75 Simplifying v = -0.75

Subproblem 2

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

Solution

v = {-0.75, 2}

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