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

Solution for 10(z+3)-4(z-3)=3(z-2)+2(z-3) equation:

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

Reorder the terms:
10(3 + z) + -4(z + -3) = 3(z + -2) + 2(z + -3)
(3 * 10 + z * 10) + -4(z + -3) = 3(z + -2) + 2(z + -3)
(30 + 10z) + -4(z + -3) = 3(z + -2) + 2(z + -3)

Reorder the terms:
30 + 10z + -4(-3 + z) = 3(z + -2) + 2(z + -3)
30 + 10z + (-3 * -4 + z * -4) = 3(z + -2) + 2(z + -3)
30 + 10z + (12 + -4z) = 3(z + -2) + 2(z + -3)

Reorder the terms:
30 + 12 + 10z + -4z = 3(z + -2) + 2(z + -3)

Combine like terms: 30 + 12 = 42
42 + 10z + -4z = 3(z + -2) + 2(z + -3)

Combine like terms: 10z + -4z = 6z
42 + 6z = 3(z + -2) + 2(z + -3)

Reorder the terms:
42 + 6z = 3(-2 + z) + 2(z + -3)
42 + 6z = (-2 * 3 + z * 3) + 2(z + -3)
42 + 6z = (-6 + 3z) + 2(z + -3)

Reorder the terms:
42 + 6z = -6 + 3z + 2(-3 + z)
42 + 6z = -6 + 3z + (-3 * 2 + z * 2)
42 + 6z = -6 + 3z + (-6 + 2z)

Reorder the terms:
42 + 6z = -6 + -6 + 3z + 2z

Combine like terms: -6 + -6 = -12
42 + 6z = -12 + 3z + 2z

Combine like terms: 3z + 2z = 5z
42 + 6z = -12 + 5z

Solving
42 + 6z = -12 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
42 + 6z + -5z = -12 + 5z + -5z

Combine like terms: 6z + -5z = 1z
42 + 1z = -12 + 5z + -5z

Combine like terms: 5z + -5z = 0
42 + 1z = -12 + 0
42 + 1z = -12

Add '-42' to each side of the equation.
42 + -42 + 1z = -12 + -42

Combine like terms: 42 + -42 = 0
0 + 1z = -12 + -42
1z = -12 + -42

Combine like terms: -12 + -42 = -54
1z = -54

Divide each side by '1'.
z = -54

Simplifying
z = -54