2(.5q+1)=-3(2q+1)+4(2q+1)

Solution for 2(.5q+1)=-3(2q+1)+4(2q+1) equation:

Simplifying
2(0.5q + 1) = -3(2q + 1) + 4(2q + 1)

Reorder the terms:
2(1 + 0.5q) = -3(2q + 1) + 4(2q + 1)
(1 * 2 + 0.5q * 2) = -3(2q + 1) + 4(2q + 1)
(2 + 1q) = -3(2q + 1) + 4(2q + 1)

Reorder the terms:
2 + 1q = -3(1 + 2q) + 4(2q + 1)
2 + 1q = (1 * -3 + 2q * -3) + 4(2q + 1)
2 + 1q = (-3 + -6q) + 4(2q + 1)

Reorder the terms:
2 + 1q = -3 + -6q + 4(1 + 2q)
2 + 1q = -3 + -6q + (1 * 4 + 2q * 4)
2 + 1q = -3 + -6q + (4 + 8q)

Reorder the terms:
2 + 1q = -3 + 4 + -6q + 8q

Combine like terms: -3 + 4 = 1
2 + 1q = 1 + -6q + 8q

Combine like terms: -6q + 8q = 2q
2 + 1q = 1 + 2q

Solving
2 + 1q = 1 + 2q

Solving for variable 'q'.

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

Add '-2q' to each side of the equation.
2 + 1q + -2q = 1 + 2q + -2q

Combine like terms: 1q + -2q = -1q
2 + -1q = 1 + 2q + -2q

Combine like terms: 2q + -2q = 0
2 + -1q = 1 + 0
2 + -1q = 1

Add '-2' to each side of the equation.
2 + -2 + -1q = 1 + -2

Combine like terms: 2 + -2 = 0
0 + -1q = 1 + -2
-1q = 1 + -2

Combine like terms: 1 + -2 = -1
-1q = -1

Divide each side by '-1'.
q = 1

Simplifying
q = 1