3(4v+1)-(2v+3)=2(v-7)+w

Solution for 3(4v+1)-(2v+3)=2(v-7)+w equation:

Simplifying
3(4v + 1) + -1(2v + 3) = 2(v + -7) + w

Reorder the terms:
3(1 + 4v) + -1(2v + 3) = 2(v + -7) + w
(1 * 3 + 4v * 3) + -1(2v + 3) = 2(v + -7) + w
(3 + 12v) + -1(2v + 3) = 2(v + -7) + w

Reorder the terms:
3 + 12v + -1(3 + 2v) = 2(v + -7) + w
3 + 12v + (3 * -1 + 2v * -1) = 2(v + -7) + w
3 + 12v + (-3 + -2v) = 2(v + -7) + w

Reorder the terms:
3 + -3 + 12v + -2v = 2(v + -7) + w

Combine like terms: 3 + -3 = 0
0 + 12v + -2v = 2(v + -7) + w
12v + -2v = 2(v + -7) + w

Combine like terms: 12v + -2v = 10v
10v = 2(v + -7) + w

Reorder the terms:
10v = 2(-7 + v) + w
10v = (-7 * 2 + v * 2) + w
10v = (-14 + 2v) + w

Solving
10v = -14 + 2v + w

Solving for variable 'v'.

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

Add '-2v' to each side of the equation.
10v + -2v = -14 + 2v + -2v + w

Combine like terms: 10v + -2v = 8v
8v = -14 + 2v + -2v + w

Combine like terms: 2v + -2v = 0
8v = -14 + 0 + w
8v = -14 + w

Divide each side by '8'.
v = -1.75 + 0.125w

Simplifying
v = -1.75 + 0.125w