2(-p+q)+3(p+2q)=0

Solution for 2(-p+q)+3(p+2q)=0 equation:

Simplifying
2(-1p + q) + 3(p + 2q) = 0
(-1p * 2 + q * 2) + 3(p + 2q) = 0
(-2p + 2q) + 3(p + 2q) = 0
-2p + 2q + (p * 3 + 2q * 3) = 0
-2p + 2q + (3p + 6q) = 0

Reorder the terms:
-2p + 3p + 2q + 6q = 0

Combine like terms: -2p + 3p = 1p
1p + 2q + 6q = 0

Combine like terms: 2q + 6q = 8q
1p + 8q = 0

Solving
1p + 8q = 0

Solving for variable 'p'.

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

Add '-8q' to each side of the equation.
1p + 8q + -8q = 0 + -8q

Combine like terms: 8q + -8q = 0
1p + 0 = 0 + -8q
1p = 0 + -8q
Remove the zero:
1p = -8q

Divide each side by '1'.
p = -8q

Simplifying
p = -8q