10(v+4)2v=2(4v+3)-13

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Solution for 10(v+4)2v=2(4v+3)-13 equation: 


Simplifying
10(v + 4) * 2v = 2(4v + 3) + -13

Reorder the terms:
10(4 + v) * 2v = 2(4v + 3) + -13

Reorder the terms for easier multiplication:
10 * 2v(4 + v) = 2(4v + 3) + -13

Multiply 10 * 2
20v(4 + v) = 2(4v + 3) + -13
(4 * 20v + v * 20v) = 2(4v + 3) + -13
(80v + 20v2) = 2(4v + 3) + -13

Reorder the terms:
80v + 20v2 = 2(3 + 4v) + -13
80v + 20v2 = (3 * 2 + 4v * 2) + -13
80v + 20v2 = (6 + 8v) + -13

Reorder the terms:
80v + 20v2 = 6 + -13 + 8v

Combine like terms: 6 + -13 = -7
80v + 20v2 = -7 + 8v

Solving
80v + 20v2 = -7 + 8v

Solving for variable 'v'.

Reorder the terms:
7 + 80v + -8v + 20v2 = -7 + 8v + 7 + -8v

Combine like terms: 80v + -8v = 72v
7 + 72v + 20v2 = -7 + 8v + 7 + -8v

Reorder the terms:
7 + 72v + 20v2 = -7 + 7 + 8v + -8v

Combine like terms: -7 + 7 = 0
7 + 72v + 20v2 = 0 + 8v + -8v
7 + 72v + 20v2 = 8v + -8v

Combine like terms: 8v + -8v = 0
7 + 72v + 20v2 = 0

Factor a trinomial.
(7 + 2v)(1 + 10v) = 0


Subproblem 1
Set the factor '(7 + 2v)' equal to zero and attempt to solve:

Simplifying
7 + 2v = 0

Solving
7 + 2v = 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 + 2v = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 2v = 0 + -7
2v = 0 + -7

Combine like terms: 0 + -7 = -7
2v = -7

Divide each side by '2'.
v = -3.5

Simplifying
v = -3.5

Subproblem 2
Set the factor '(1 + 10v)' equal to zero and attempt to solve:

Simplifying
1 + 10v = 0

Solving
1 + 10v = 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 + 10v = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 10v = 0 + -1
10v = 0 + -1

Combine like terms: 0 + -1 = -1
10v = -1

Divide each side by '10'.
v = -0.1

Simplifying
v = -0.1
Solution
v = {-3.5, -0.1}

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