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

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

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

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

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

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

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

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

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

Reorder the terms:
49 + 7z = -4 + 4z + 2(-4 + z)
49 + 7z = -4 + 4z + (-4 * 2 + z * 2)
49 + 7z = -4 + 4z + (-8 + 2z)

Reorder the terms:
49 + 7z = -4 + -8 + 4z + 2z

Combine like terms: -4 + -8 = -12
49 + 7z = -12 + 4z + 2z

Combine like terms: 4z + 2z = 6z
49 + 7z = -12 + 6z

Solving
49 + 7z = -12 + 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 = -12 + 6z + -6z

Combine like terms: 7z + -6z = 1z
49 + 1z = -12 + 6z + -6z

Combine like terms: 6z + -6z = 0
49 + 1z = -12 + 0
49 + 1z = -12

Add '-49' to each side of the equation.
49 + -49 + 1z = -12 + -49

Combine like terms: 49 + -49 = 0
0 + 1z = -12 + -49
1z = -12 + -49

Combine like terms: -12 + -49 = -61
1z = -61

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

Simplifying
z = -61