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

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

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

Reorder the terms:
10(2 + z) + -4(z + -4) = 3(z + -3) + 2(z + -2)
(2 * 10 + z * 10) + -4(z + -4) = 3(z + -3) + 2(z + -2)
(20 + 10z) + -4(z + -4) = 3(z + -3) + 2(z + -2)

Reorder the terms:
20 + 10z + -4(-4 + z) = 3(z + -3) + 2(z + -2)
20 + 10z + (-4 * -4 + z * -4) = 3(z + -3) + 2(z + -2)
20 + 10z + (16 + -4z) = 3(z + -3) + 2(z + -2)

Reorder the terms:
20 + 16 + 10z + -4z = 3(z + -3) + 2(z + -2)

Combine like terms: 20 + 16 = 36
36 + 10z + -4z = 3(z + -3) + 2(z + -2)

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

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

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

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

Combine like terms: -9 + -4 = -13
36 + 6z = -13 + 3z + 2z

Combine like terms: 3z + 2z = 5z
36 + 6z = -13 + 5z

Solving
36 + 6z = -13 + 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.
36 + 6z + -5z = -13 + 5z + -5z

Combine like terms: 6z + -5z = 1z
36 + 1z = -13 + 5z + -5z

Combine like terms: 5z + -5z = 0
36 + 1z = -13 + 0
36 + 1z = -13

Add '-36' to each side of the equation.
36 + -36 + 1z = -13 + -36

Combine like terms: 36 + -36 = 0
0 + 1z = -13 + -36
1z = -13 + -36

Combine like terms: -13 + -36 = -49
1z = -49

Divide each side by '1'.
z = -49

Simplifying
z = -49