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 = 23
1z = 23

Divide each side by '1'.
z = 23

Simplifying
z = 23