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

Solution for 9(z+4)-2(z-3)=2(z-4)+4(z-2) equation:

Simplifying
9(z + 4) + -2(z + -3) = 2(z + -4) + 4(z + -2)

Reorder the terms:
9(4 + z) + -2(z + -3) = 2(z + -4) + 4(z + -2)
(4 * 9 + z * 9) + -2(z + -3) = 2(z + -4) + 4(z + -2)
(36 + 9z) + -2(z + -3) = 2(z + -4) + 4(z + -2)

Reorder the terms:
36 + 9z + -2(-3 + z) = 2(z + -4) + 4(z + -2)
36 + 9z + (-3 * -2 + z * -2) = 2(z + -4) + 4(z + -2)
36 + 9z + (6 + -2z) = 2(z + -4) + 4(z + -2)

Reorder the terms:
36 + 6 + 9z + -2z = 2(z + -4) + 4(z + -2)

Combine like terms: 36 + 6 = 42
42 + 9z + -2z = 2(z + -4) + 4(z + -2)

Combine like terms: 9z + -2z = 7z
42 + 7z = 2(z + -4) + 4(z + -2)

Reorder the terms:
42 + 7z = 2(-4 + z) + 4(z + -2)
42 + 7z = (-4 * 2 + z * 2) + 4(z + -2)
42 + 7z = (-8 + 2z) + 4(z + -2)

Reorder the terms:
42 + 7z = -8 + 2z + 4(-2 + z)
42 + 7z = -8 + 2z + (-2 * 4 + z * 4)
42 + 7z = -8 + 2z + (-8 + 4z)

Reorder the terms:
42 + 7z = -8 + -8 + 2z + 4z

Combine like terms: -8 + -8 = -16
42 + 7z = -16 + 2z + 4z

Combine like terms: 2z + 4z = 6z
42 + 7z = -16 + 6z

Solving
42 + 7z = -16 + 6z

Solving for variable 'z'.

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

Add '-6z' to each side of the equation.
42 + 7z + -6z = -16 + 6z + -6z

Combine like terms: 7z + -6z = 1z
42 + 1z = -16 + 6z + -6z

Combine like terms: 6z + -6z = 0
42 + 1z = -16 + 0
42 + 1z = -16

Add '-42' to each side of the equation.
42 + -42 + 1z = -16 + -42

Combine like terms: 42 + -42 = 0
0 + 1z = -16 + -42
1z = -16 + -42

Combine like terms: -16 + -42 = -58
1z = -58

Divide each side by '1'.
z = -58

Simplifying
z = -58