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

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

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

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

Reorder the terms:
40 + 10z + -3(-3 + z) = 2(z + -2) + 4(z + -1)
40 + 10z + (-3 * -3 + z * -3) = 2(z + -2) + 4(z + -1)
40 + 10z + (9 + -3z) = 2(z + -2) + 4(z + -1)

Reorder the terms:
40 + 9 + 10z + -3z = 2(z + -2) + 4(z + -1)

Combine like terms: 40 + 9 = 49
49 + 10z + -3z = 2(z + -2) + 4(z + -1)

Combine like terms: 10z + -3z = 7z
49 + 7z = 2(z + -2) + 4(z + -1)

Reorder the terms:
49 + 7z = 2(-2 + z) + 4(z + -1)
49 + 7z = (-2 * 2 + z * 2) + 4(z + -1)
49 + 7z = (-4 + 2z) + 4(z + -1)

Reorder the terms:
49 + 7z = -4 + 2z + 4(-1 + z)
49 + 7z = -4 + 2z + (-1 * 4 + z * 4)
49 + 7z = -4 + 2z + (-4 + 4z)

Reorder the terms:
49 + 7z = -4 + -4 + 2z + 4z

Combine like terms: -4 + -4 = -8
49 + 7z = -8 + 2z + 4z

Combine like terms: 2z + 4z = 6z
49 + 7z = -8 + 6z

Solving
49 + 7z = -8 + 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.
49 + 7z + -6z = -8 + 6z + -6z

Combine like terms: 7z + -6z = 1z
49 + 1z = -8 + 6z + -6z

Combine like terms: 6z + -6z = 0
49 + 1z = -8 + 0
49 + 1z = -8

Add '-49' to each side of the equation.
49 + -49 + 1z = -8 + -49

Combine like terms: 49 + -49 = 0
0 + 1z = -8 + -49
1z = -8 + -49

Combine like terms: -8 + -49 = -57
1z = -57

Divide each side by '1'.
z = -57

Simplifying
z = -57