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

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

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

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

Reorder the terms:
20 + 10z + -3(-4 + z) = 3(z + -3) + 3(z + -2)
20 + 10z + (-4 * -3 + z * -3) = 3(z + -3) + 3(z + -2)
20 + 10z + (12 + -3z) = 3(z + -3) + 3(z + -2)

Reorder the terms:
20 + 12 + 10z + -3z = 3(z + -3) + 3(z + -2)

Combine like terms: 20 + 12 = 32
32 + 10z + -3z = 3(z + -3) + 3(z + -2)

Combine like terms: 10z + -3z = 7z
32 + 7z = 3(z + -3) + 3(z + -2)

Reorder the terms:
32 + 7z = 3(-3 + z) + 3(z + -2)
32 + 7z = (-3 * 3 + z * 3) + 3(z + -2)
32 + 7z = (-9 + 3z) + 3(z + -2)

Reorder the terms:
32 + 7z = -9 + 3z + 3(-2 + z)
32 + 7z = -9 + 3z + (-2 * 3 + z * 3)
32 + 7z = -9 + 3z + (-6 + 3z)

Reorder the terms:
32 + 7z = -9 + -6 + 3z + 3z

Combine like terms: -9 + -6 = -15
32 + 7z = -15 + 3z + 3z

Combine like terms: 3z + 3z = 6z
32 + 7z = -15 + 6z

Solving
32 + 7z = -15 + 6z

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-6z' to each side of the equation.
32 + 7z + -6z = -15 + 6z + -6z

Combine like terms: 7z + -6z = 1z
32 + 1z = -15 + 6z + -6z

Combine like terms: 6z + -6z = 0
32 + 1z = -15 + 0
32 + 1z = -15

Add '-32' to each side of the equation.
32 + -32 + 1z = -15 + -32

Combine like terms: 32 + -32 = 0
0 + 1z = -15 + -32
1z = -15 + -32

Combine like terms: -15 + -32 = -47
1z = -47

Divide each side by '1'.
z = -47

Simplifying
z = -47