(12v+7)(5v-2)=0

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Solution for (12v+7)(5v-2)=0 equation: 


Simplifying
(12v + 7)(5v + -2) = 0

Reorder the terms:
(7 + 12v)(5v + -2) = 0

Reorder the terms:
(7 + 12v)(-2 + 5v) = 0

Multiply (7 + 12v) * (-2 + 5v)
(7(-2 + 5v) + 12v * (-2 + 5v)) = 0
((-2 * 7 + 5v * 7) + 12v * (-2 + 5v)) = 0
((-14 + 35v) + 12v * (-2 + 5v)) = 0
(-14 + 35v + (-2 * 12v + 5v * 12v)) = 0
(-14 + 35v + (-24v + 60v2)) = 0

Combine like terms: 35v + -24v = 11v
(-14 + 11v + 60v2) = 0

Solving
-14 + 11v + 60v2 = 0

Solving for variable 'v'.

Factor a trinomial.
(-7 + -12v)(2 + -5v) = 0


Subproblem 1
Set the factor '(-7 + -12v)' equal to zero and attempt to solve:

Simplifying
-7 + -12v = 0

Solving
-7 + -12v = 0

Move all terms containing v to the left, all other terms to the right.

Add '7' to each side of the equation.
-7 + 7 + -12v = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12v = 0 + 7
-12v = 0 + 7

Combine like terms: 0 + 7 = 7
-12v = 7

Divide each side by '-12'.
v = -0.5833333333

Simplifying
v = -0.5833333333

Subproblem 2
Set the factor '(2 + -5v)' equal to zero and attempt to solve:

Simplifying
2 + -5v = 0

Solving
2 + -5v = 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 + -5v = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5v = 0 + -2
-5v = 0 + -2

Combine like terms: 0 + -2 = -2
-5v = -2

Divide each side by '-5'.
v = 0.4

Simplifying
v = 0.4
Solution
v = {-0.5833333333, 0.4}

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