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

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

Simplifying
4z + 3(5 + -1z) = -1(z + -4) + 1
4z + (5 * 3 + -1z * 3) = -1(z + -4) + 1
4z + (15 + -3z) = -1(z + -4) + 1

Reorder the terms:
15 + 4z + -3z = -1(z + -4) + 1

Combine like terms: 4z + -3z = 1z
15 + 1z = -1(z + -4) + 1

Reorder the terms:
15 + 1z = -1(-4 + z) + 1
15 + 1z = (-4 * -1 + z * -1) + 1
15 + 1z = (4 + -1z) + 1

Reorder the terms:
15 + 1z = 4 + 1 + -1z

Combine like terms: 4 + 1 = 5
15 + 1z = 5 + -1z

Solving
15 + 1z = 5 + -1z

Solving for variable 'z'.

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

Add 'z' to each side of the equation.
15 + 1z + z = 5 + -1z + z

Combine like terms: 1z + z = 2z
15 + 2z = 5 + -1z + z

Combine like terms: -1z + z = 0
15 + 2z = 5 + 0
15 + 2z = 5

Add '-15' to each side of the equation.
15 + -15 + 2z = 5 + -15

Combine like terms: 15 + -15 = 0
0 + 2z = 5 + -15
2z = 5 + -15

Combine like terms: 5 + -15 = -10
2z = -10

Divide each side by '2'.
z = -5

Simplifying
z = -5