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

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

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

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

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

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

Combine like terms: 30 + 4 = 34
34 + 10z + -2z = 3(z + -4) + 4(z + -4)

Combine like terms: 10z + -2z = 8z
34 + 8z = 3(z + -4) + 4(z + -4)

Reorder the terms:
34 + 8z = 3(-4 + z) + 4(z + -4)
34 + 8z = (-4 * 3 + z * 3) + 4(z + -4)
34 + 8z = (-12 + 3z) + 4(z + -4)

Reorder the terms:
34 + 8z = -12 + 3z + 4(-4 + z)
34 + 8z = -12 + 3z + (-4 * 4 + z * 4)
34 + 8z = -12 + 3z + (-16 + 4z)

Reorder the terms:
34 + 8z = -12 + -16 + 3z + 4z

Combine like terms: -12 + -16 = -28
34 + 8z = -28 + 3z + 4z

Combine like terms: 3z + 4z = 7z
34 + 8z = -28 + 7z

Solving
34 + 8z = -28 + 7z

Solving for variable 'z'.

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

Add '-7z' to each side of the equation.
34 + 8z + -7z = -28 + 7z + -7z

Combine like terms: 8z + -7z = 1z
34 + 1z = -28 + 7z + -7z

Combine like terms: 7z + -7z = 0
34 + 1z = -28 + 0
34 + 1z = -28

Add '-34' to each side of the equation.
34 + -34 + 1z = -28 + -34

Combine like terms: 34 + -34 = 0
0 + 1z = -28 + -34
1z = -28 + -34

Combine like terms: -28 + -34 = -62
1z = -62

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

Simplifying
z = -62