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

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

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

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

Reorder the terms:
30 + 10z + -2(-3 + z) = 4(z + -3) + 3(z + -2)
30 + 10z + (-3 * -2 + z * -2) = 4(z + -3) + 3(z + -2)
30 + 10z + (6 + -2z) = 4(z + -3) + 3(z + -2)

Reorder the terms:
30 + 6 + 10z + -2z = 4(z + -3) + 3(z + -2)

Combine like terms: 30 + 6 = 36
36 + 10z + -2z = 4(z + -3) + 3(z + -2)

Combine like terms: 10z + -2z = 8z
36 + 8z = 4(z + -3) + 3(z + -2)

Reorder the terms:
36 + 8z = 4(-3 + z) + 3(z + -2)
36 + 8z = (-3 * 4 + z * 4) + 3(z + -2)
36 + 8z = (-12 + 4z) + 3(z + -2)

Reorder the terms:
36 + 8z = -12 + 4z + 3(-2 + z)
36 + 8z = -12 + 4z + (-2 * 3 + z * 3)
36 + 8z = -12 + 4z + (-6 + 3z)

Reorder the terms:
36 + 8z = -12 + -6 + 4z + 3z

Combine like terms: -12 + -6 = -18
36 + 8z = -18 + 4z + 3z

Combine like terms: 4z + 3z = 7z
36 + 8z = -18 + 7z

Solving
36 + 8z = -18 + 7z

Solving for variable 'z'.

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

Add '-7z' to each side of the equation.
36 + 8z + -7z = -18 + 7z + -7z

Combine like terms: 8z + -7z = 1z
36 + 1z = -18 + 7z + -7z

Combine like terms: 7z + -7z = 0
36 + 1z = -18 + 0
36 + 1z = -18

Add '-36' to each side of the equation.
36 + -36 + 1z = -18 + -36

Combine like terms: 36 + -36 = 0
0 + 1z = -18 + -36
1z = -18 + -36

Combine like terms: -18 + -36 = -54
1z = -54

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

Simplifying
z = -54