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

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

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

Reorder the terms:
10(4 + z) + -4(z + 2) = 3(z + -1) + 2(z + -3)
(4 * 10 + z * 10) + -4(z + 2) = 3(z + -1) + 2(z + -3)
(40 + 10z) + -4(z + 2) = 3(z + -1) + 2(z + -3)

Reorder the terms:
40 + 10z + -4(2 + z) = 3(z + -1) + 2(z + -3)
40 + 10z + (2 * -4 + z * -4) = 3(z + -1) + 2(z + -3)
40 + 10z + (-8 + -4z) = 3(z + -1) + 2(z + -3)

Reorder the terms:
40 + -8 + 10z + -4z = 3(z + -1) + 2(z + -3)

Combine like terms: 40 + -8 = 32
32 + 10z + -4z = 3(z + -1) + 2(z + -3)

Combine like terms: 10z + -4z = 6z
32 + 6z = 3(z + -1) + 2(z + -3)

Reorder the terms:
32 + 6z = 3(-1 + z) + 2(z + -3)
32 + 6z = (-1 * 3 + z * 3) + 2(z + -3)
32 + 6z = (-3 + 3z) + 2(z + -3)

Reorder the terms:
32 + 6z = -3 + 3z + 2(-3 + z)
32 + 6z = -3 + 3z + (-3 * 2 + z * 2)
32 + 6z = -3 + 3z + (-6 + 2z)

Reorder the terms:
32 + 6z = -3 + -6 + 3z + 2z

Combine like terms: -3 + -6 = -9
32 + 6z = -9 + 3z + 2z

Combine like terms: 3z + 2z = 5z
32 + 6z = -9 + 5z

Solving
32 + 6z = -9 + 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.
32 + 6z + -5z = -9 + 5z + -5z

Combine like terms: 6z + -5z = 1z
32 + 1z = -9 + 5z + -5z

Combine like terms: 5z + -5z = 0
32 + 1z = -9 + 0
32 + 1z = -9

Add '-32' to each side of the equation.
32 + -32 + 1z = -9 + -32

Combine like terms: 32 + -32 = 0
0 + 1z = -9 + -32
1z = -9 + -32

Combine like terms: -9 + -32 = -41
1z = -41

Divide each side by '1'.
z = -41

Simplifying
z = -41