5(3v+7)(5v+1)=0

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Solution for 5(3v+7)(5v+1)=0 equation: 


Simplifying
5(3v + 7)(5v + 1) = 0

Reorder the terms:
5(7 + 3v)(5v + 1) = 0

Reorder the terms:
5(7 + 3v)(1 + 5v) = 0

Multiply (7 + 3v) * (1 + 5v)
5(7(1 + 5v) + 3v * (1 + 5v)) = 0
5((1 * 7 + 5v * 7) + 3v * (1 + 5v)) = 0
5((7 + 35v) + 3v * (1 + 5v)) = 0
5(7 + 35v + (1 * 3v + 5v * 3v)) = 0
5(7 + 35v + (3v + 15v2)) = 0

Combine like terms: 35v + 3v = 38v
5(7 + 38v + 15v2) = 0
(7 * 5 + 38v * 5 + 15v2 * 5) = 0
(35 + 190v + 75v2) = 0

Solving
35 + 190v + 75v2 = 0

Solving for variable 'v'.

Factor out the Greatest Common Factor (GCF), '5'.
5(7 + 38v + 15v2) = 0

Factor a trinomial.
5((7 + 3v)(1 + 5v)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(7 + 3v)' equal to zero and attempt to solve:

Simplifying
7 + 3v = 0

Solving
7 + 3v = 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 + 3v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3v = 0 + -7
3v = 0 + -7

Combine like terms: 0 + -7 = -7
3v = -7

Divide each side by '3'.
v = -2.333333333

Simplifying
v = -2.333333333

Subproblem 2
Set the factor '(1 + 5v)' equal to zero and attempt to solve:

Simplifying
1 + 5v = 0

Solving
1 + 5v = 0

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

Add '-1' to each side of the equation.
1 + -1 + 5v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5v = 0 + -1
5v = 0 + -1

Combine like terms: 0 + -1 = -1
5v = -1

Divide each side by '5'.
v = -0.2

Simplifying
v = -0.2
Solution
v = {-2.333333333, -0.2}

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