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

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

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

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

Reorder the terms:
30 + 10z + -4(-2 + z) = 3(z + -4) + 2(z + -4)
30 + 10z + (-2 * -4 + z * -4) = 3(z + -4) + 2(z + -4)
30 + 10z + (8 + -4z) = 3(z + -4) + 2(z + -4)

Reorder the terms:
30 + 8 + 10z + -4z = 3(z + -4) + 2(z + -4)

Combine like terms: 30 + 8 = 38
38 + 10z + -4z = 3(z + -4) + 2(z + -4)

Combine like terms: 10z + -4z = 6z
38 + 6z = 3(z + -4) + 2(z + -4)

Reorder the terms:
38 + 6z = 3(-4 + z) + 2(z + -4)
38 + 6z = (-4 * 3 + z * 3) + 2(z + -4)
38 + 6z = (-12 + 3z) + 2(z + -4)

Reorder the terms:
38 + 6z = -12 + 3z + 2(-4 + z)
38 + 6z = -12 + 3z + (-4 * 2 + z * 2)
38 + 6z = -12 + 3z + (-8 + 2z)

Reorder the terms:
38 + 6z = -12 + -8 + 3z + 2z

Combine like terms: -12 + -8 = -20
38 + 6z = -20 + 3z + 2z

Combine like terms: 3z + 2z = 5z
38 + 6z = -20 + 5z

Solving
38 + 6z = -20 + 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.
38 + 6z + -5z = -20 + 5z + -5z

Combine like terms: 6z + -5z = 1z
38 + 1z = -20 + 5z + -5z

Combine like terms: 5z + -5z = 0
38 + 1z = -20 + 0
38 + 1z = -20

Add '-38' to each side of the equation.
38 + -38 + 1z = -20 + -38

Combine like terms: 38 + -38 = 0
0 + 1z = -20 + -38
1z = -20 + -38

Combine like terms: -20 + -38 = -58
1z = -58

Divide each side by '1'.
z = -58

Simplifying
z = -58