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

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

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

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

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

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

Combine like terms: 40 + 4 = 44
44 + 10z + -2z = 3(z + -3) + 4(z + -2)

Combine like terms: 10z + -2z = 8z
44 + 8z = 3(z + -3) + 4(z + -2)

Reorder the terms:
44 + 8z = 3(-3 + z) + 4(z + -2)
44 + 8z = (-3 * 3 + z * 3) + 4(z + -2)
44 + 8z = (-9 + 3z) + 4(z + -2)

Reorder the terms:
44 + 8z = -9 + 3z + 4(-2 + z)
44 + 8z = -9 + 3z + (-2 * 4 + z * 4)
44 + 8z = -9 + 3z + (-8 + 4z)

Reorder the terms:
44 + 8z = -9 + -8 + 3z + 4z

Combine like terms: -9 + -8 = -17
44 + 8z = -17 + 3z + 4z

Combine like terms: 3z + 4z = 7z
44 + 8z = -17 + 7z

Solving
44 + 8z = -17 + 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.
44 + 8z + -7z = -17 + 7z + -7z

Combine like terms: 8z + -7z = 1z
44 + 1z = -17 + 7z + -7z

Combine like terms: 7z + -7z = 0
44 + 1z = -17 + 0
44 + 1z = -17

Add '-44' to each side of the equation.
44 + -44 + 1z = -17 + -44

Combine like terms: 44 + -44 = 0
0 + 1z = -17 + -44
1z = -17 + -44

Combine like terms: -17 + -44 = -61
1z = -61

Divide each side by '1'.
z = -61

Simplifying
z = -61