10(z+1)-4(z-2)=2(z-3)+3(z-3)

Solution for 10(z+1)-4(z-2)=2(z-3)+3(z-3) equation:

Simplifying
10(z + 1) + -4(z + -2) = 2(z + -3) + 3(z + -3)

Reorder the terms:
10(1 + z) + -4(z + -2) = 2(z + -3) + 3(z + -3)
(1 * 10 + z * 10) + -4(z + -2) = 2(z + -3) + 3(z + -3)
(10 + 10z) + -4(z + -2) = 2(z + -3) + 3(z + -3)

Reorder the terms:
10 + 10z + -4(-2 + z) = 2(z + -3) + 3(z + -3)
10 + 10z + (-2 * -4 + z * -4) = 2(z + -3) + 3(z + -3)
10 + 10z + (8 + -4z) = 2(z + -3) + 3(z + -3)

Reorder the terms:
10 + 8 + 10z + -4z = 2(z + -3) + 3(z + -3)

Combine like terms: 10 + 8 = 18
18 + 10z + -4z = 2(z + -3) + 3(z + -3)

Combine like terms: 10z + -4z = 6z
18 + 6z = 2(z + -3) + 3(z + -3)

Reorder the terms:
18 + 6z = 2(-3 + z) + 3(z + -3)
18 + 6z = (-3 * 2 + z * 2) + 3(z + -3)
18 + 6z = (-6 + 2z) + 3(z + -3)

Reorder the terms:
18 + 6z = -6 + 2z + 3(-3 + z)
18 + 6z = -6 + 2z + (-3 * 3 + z * 3)
18 + 6z = -6 + 2z + (-9 + 3z)

Reorder the terms:
18 + 6z = -6 + -9 + 2z + 3z

Combine like terms: -6 + -9 = -15
18 + 6z = -15 + 2z + 3z

Combine like terms: 2z + 3z = 5z
18 + 6z = -15 + 5z

Solving
18 + 6z = -15 + 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.
18 + 6z + -5z = -15 + 5z + -5z

Combine like terms: 6z + -5z = 1z
18 + 1z = -15 + 5z + -5z

Combine like terms: 5z + -5z = 0
18 + 1z = -15 + 0
18 + 1z = -15

Add '-18' to each side of the equation.
18 + -18 + 1z = -15 + -18

Combine like terms: 18 + -18 = 0
0 + 1z = -15 + -18
1z = -15 + -18

Combine like terms: -15 + -18 = -33
1z = -33

Divide each side by '1'.
z = -33

Simplifying
z = -33