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

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

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

Reorder the terms:
10(4 + z) + -4(z + -3) = 3(z + -2) + 2(z + -2)
(4 * 10 + z * 10) + -4(z + -3) = 3(z + -2) + 2(z + -2)
(40 + 10z) + -4(z + -3) = 3(z + -2) + 2(z + -2)

Reorder the terms:
40 + 10z + -4(-3 + z) = 3(z + -2) + 2(z + -2)
40 + 10z + (-3 * -4 + z * -4) = 3(z + -2) + 2(z + -2)
40 + 10z + (12 + -4z) = 3(z + -2) + 2(z + -2)

Reorder the terms:
40 + 12 + 10z + -4z = 3(z + -2) + 2(z + -2)

Combine like terms: 40 + 12 = 52
52 + 10z + -4z = 3(z + -2) + 2(z + -2)

Combine like terms: 10z + -4z = 6z
52 + 6z = 3(z + -2) + 2(z + -2)

Reorder the terms:
52 + 6z = 3(-2 + z) + 2(z + -2)
52 + 6z = (-2 * 3 + z * 3) + 2(z + -2)
52 + 6z = (-6 + 3z) + 2(z + -2)

Reorder the terms:
52 + 6z = -6 + 3z + 2(-2 + z)
52 + 6z = -6 + 3z + (-2 * 2 + z * 2)
52 + 6z = -6 + 3z + (-4 + 2z)

Reorder the terms:
52 + 6z = -6 + -4 + 3z + 2z

Combine like terms: -6 + -4 = -10
52 + 6z = -10 + 3z + 2z

Combine like terms: 3z + 2z = 5z
52 + 6z = -10 + 5z

Solving
52 + 6z = -10 + 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.
52 + 6z + -5z = -10 + 5z + -5z

Combine like terms: 6z + -5z = 1z
52 + 1z = -10 + 5z + -5z

Combine like terms: 5z + -5z = 0
52 + 1z = -10 + 0
52 + 1z = -10

Add '-52' to each side of the equation.
52 + -52 + 1z = -10 + -52

Combine like terms: 52 + -52 = 0
0 + 1z = -10 + -52
1z = -10 + -52

Combine like terms: -10 + -52 = -62
1z = -62

Divide each side by '1'.
z = -62

Simplifying
z = -62