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

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

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

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

Reorder the terms:
3 + 12v + -3(3 + 2v) = 2(v + -7) + w
3 + 12v + (3 * -3 + 2v * -3) = 2(v + -7) + w
3 + 12v + (-9 + -6v) = 2(v + -7) + w

Reorder the terms:
3 + -9 + 12v + -6v = 2(v + -7) + w

Combine like terms: 3 + -9 = -6
-6 + 12v + -6v = 2(v + -7) + w

Combine like terms: 12v + -6v = 6v
-6 + 6v = 2(v + -7) + w

Reorder the terms:
-6 + 6v = 2(-7 + v) + w
-6 + 6v = (-7 * 2 + v * 2) + w
-6 + 6v = (-14 + 2v) + w

Solving
-6 + 6v = -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.
-6 + 6v + -2v = -14 + 2v + -2v + w

Combine like terms: 6v + -2v = 4v
-6 + 4v = -14 + 2v + -2v + w

Combine like terms: 2v + -2v = 0
-6 + 4v = -14 + 0 + w
-6 + 4v = -14 + w

Add '6' to each side of the equation.
-6 + 6 + 4v = -14 + 6 + w

Combine like terms: -6 + 6 = 0
0 + 4v = -14 + 6 + w
4v = -14 + 6 + w

Combine like terms: -14 + 6 = -8
4v = -8 + w

Divide each side by '4'.
v = -2 + 0.25w

Simplifying
v = -2 + 0.25w