2(1-z)+3(z+3)=4z+1

Solution for 2(1-z)+3(z+3)=4z+1 equation:

Simplifying
2(1 + -1z) + 3(z + 3) = 4z + 1
(1 * 2 + -1z * 2) + 3(z + 3) = 4z + 1
(2 + -2z) + 3(z + 3) = 4z + 1

Reorder the terms:
2 + -2z + 3(3 + z) = 4z + 1
2 + -2z + (3 * 3 + z * 3) = 4z + 1
2 + -2z + (9 + 3z) = 4z + 1

Reorder the terms:
2 + 9 + -2z + 3z = 4z + 1

Combine like terms: 2 + 9 = 11
11 + -2z + 3z = 4z + 1

Combine like terms: -2z + 3z = 1z
11 + 1z = 4z + 1

Reorder the terms:
11 + 1z = 1 + 4z

Solving
11 + 1z = 1 + 4z

Solving for variable 'z'.

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

Add '-4z' to each side of the equation.
11 + 1z + -4z = 1 + 4z + -4z

Combine like terms: 1z + -4z = -3z
11 + -3z = 1 + 4z + -4z

Combine like terms: 4z + -4z = 0
11 + -3z = 1 + 0
11 + -3z = 1

Add '-11' to each side of the equation.
11 + -11 + -3z = 1 + -11

Combine like terms: 11 + -11 = 0
0 + -3z = 1 + -11
-3z = 1 + -11

Combine like terms: 1 + -11 = -10
-3z = -10

Divide each side by '-3'.
z = 3.333333333

Simplifying
z = 3.333333333