3(z+1)+4(z-m)=5

Solution for 3(z+1)+4(z-m)=5 equation:

Simplifying
3(z + 1) + 4(z + -1m) = 5

Reorder the terms:
3(1 + z) + 4(z + -1m) = 5
(1 * 3 + z * 3) + 4(z + -1m) = 5
(3 + 3z) + 4(z + -1m) = 5

Reorder the terms:
3 + 3z + 4(-1m + z) = 5
3 + 3z + (-1m * 4 + z * 4) = 5
3 + 3z + (-4m + 4z) = 5

Reorder the terms:
3 + -4m + 3z + 4z = 5

Combine like terms: 3z + 4z = 7z
3 + -4m + 7z = 5

Solving
3 + -4m + 7z = 5

Solving for variable 'm'.

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

Add '-3' to each side of the equation.
3 + -4m + -3 + 7z = 5 + -3

Reorder the terms:
3 + -3 + -4m + 7z = 5 + -3

Combine like terms: 3 + -3 = 0
0 + -4m + 7z = 5 + -3
-4m + 7z = 5 + -3

Combine like terms: 5 + -3 = 2
-4m + 7z = 2

Add '-7z' to each side of the equation.
-4m + 7z + -7z = 2 + -7z

Combine like terms: 7z + -7z = 0
-4m + 0 = 2 + -7z
-4m = 2 + -7z

Divide each side by '-4'.
m = -0.5 + 1.75z

Simplifying
m = -0.5 + 1.75z