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

Solution for 10(z+3)-3(z-2)=3(z-2)+3(z-1) equation:

Simplifying
10(z + 3) + -3(z + -2) = 3(z + -2) + 3(z + -1)

Reorder the terms:
10(3 + z) + -3(z + -2) = 3(z + -2) + 3(z + -1)
(3 * 10 + z * 10) + -3(z + -2) = 3(z + -2) + 3(z + -1)
(30 + 10z) + -3(z + -2) = 3(z + -2) + 3(z + -1)

Reorder the terms:
30 + 10z + -3(-2 + z) = 3(z + -2) + 3(z + -1)
30 + 10z + (-2 * -3 + z * -3) = 3(z + -2) + 3(z + -1)
30 + 10z + (6 + -3z) = 3(z + -2) + 3(z + -1)

Reorder the terms:
30 + 6 + 10z + -3z = 3(z + -2) + 3(z + -1)

Combine like terms: 30 + 6 = 36
36 + 10z + -3z = 3(z + -2) + 3(z + -1)

Combine like terms: 10z + -3z = 7z
36 + 7z = 3(z + -2) + 3(z + -1)

Reorder the terms:
36 + 7z = 3(-2 + z) + 3(z + -1)
36 + 7z = (-2 * 3 + z * 3) + 3(z + -1)
36 + 7z = (-6 + 3z) + 3(z + -1)

Reorder the terms:
36 + 7z = -6 + 3z + 3(-1 + z)
36 + 7z = -6 + 3z + (-1 * 3 + z * 3)
36 + 7z = -6 + 3z + (-3 + 3z)

Reorder the terms:
36 + 7z = -6 + -3 + 3z + 3z

Combine like terms: -6 + -3 = -9
36 + 7z = -9 + 3z + 3z

Combine like terms: 3z + 3z = 6z
36 + 7z = -9 + 6z

Solving
36 + 7z = -9 + 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.
36 + 7z + -6z = -9 + 6z + -6z

Combine like terms: 7z + -6z = 1z
36 + 1z = -9 + 6z + -6z

Combine like terms: 6z + -6z = 0
36 + 1z = -9 + 0
36 + 1z = -9

Add '-36' to each side of the equation.
36 + -36 + 1z = -9 + -36

Combine like terms: 36 + -36 = 0
0 + 1z = -9 + -36
1z = -9 + -36

Combine like terms: -9 + -36 = -45
1z = -45

Divide each side by '1'.
z = -45

Simplifying
z = -45