4(2v+1)-2(3v+5)=4(v-3)+w

Solution for 4(2v+1)-2(3v+5)=4(v-3)+w equation:

Simplifying
4(2v + 1) + -2(3v + 5) = 4(v + -3) + w

Reorder the terms:
4(1 + 2v) + -2(3v + 5) = 4(v + -3) + w
(1 * 4 + 2v * 4) + -2(3v + 5) = 4(v + -3) + w
(4 + 8v) + -2(3v + 5) = 4(v + -3) + w

Reorder the terms:
4 + 8v + -2(5 + 3v) = 4(v + -3) + w
4 + 8v + (5 * -2 + 3v * -2) = 4(v + -3) + w
4 + 8v + (-10 + -6v) = 4(v + -3) + w

Reorder the terms:
4 + -10 + 8v + -6v = 4(v + -3) + w

Combine like terms: 4 + -10 = -6
-6 + 8v + -6v = 4(v + -3) + w

Combine like terms: 8v + -6v = 2v
-6 + 2v = 4(v + -3) + w

Reorder the terms:
-6 + 2v = 4(-3 + v) + w
-6 + 2v = (-3 * 4 + v * 4) + w
-6 + 2v = (-12 + 4v) + w

Solving
-6 + 2v = -12 + 4v + w

Solving for variable 'v'.

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

Add '-4v' to each side of the equation.
-6 + 2v + -4v = -12 + 4v + -4v + w

Combine like terms: 2v + -4v = -2v
-6 + -2v = -12 + 4v + -4v + w

Combine like terms: 4v + -4v = 0
-6 + -2v = -12 + 0 + w
-6 + -2v = -12 + w

Add '6' to each side of the equation.
-6 + 6 + -2v = -12 + 6 + w

Combine like terms: -6 + 6 = 0
0 + -2v = -12 + 6 + w
-2v = -12 + 6 + w

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

Divide each side by '-2'.
v = 3 + -0.5w

Simplifying
v = 3 + -0.5w