4(q)+(-1)(1-q)=1(q)+2(1-q)

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

Simplifying
4(q) + (-1)(1 + -1q) = 1(q) + 2(1 + -1q)
4q + (1 * -1 + -1q * -1) = 1(q) + 2(1 + -1q)
4q + (-1 + 1q) = 1(q) + 2(1 + -1q)

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

Combine like terms: 4q + 1q = 5q
-1 + 5q = 1(q) + 2(1 + -1q)
-1 + 5q = 1q + (1 * 2 + -1q * 2)
-1 + 5q = 1q + (2 + -2q)

Reorder the terms:
-1 + 5q = 2 + 1q + -2q

Combine like terms: 1q + -2q = -1q
-1 + 5q = 2 + -1q

Solving
-1 + 5q = 2 + -1q

Solving for variable 'q'.

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

Add 'q' to each side of the equation.
-1 + 5q + q = 2 + -1q + q

Combine like terms: 5q + q = 6q
-1 + 6q = 2 + -1q + q

Combine like terms: -1q + q = 0
-1 + 6q = 2 + 0
-1 + 6q = 2

Add '1' to each side of the equation.
-1 + 1 + 6q = 2 + 1

Combine like terms: -1 + 1 = 0
0 + 6q = 2 + 1
6q = 2 + 1

Combine like terms: 2 + 1 = 3
6q = 3

Divide each side by '6'.
q = 0.5

Simplifying
q = 0.5