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

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

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

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

Reorder the terms:
20 + 10z + -3(-2 + z) = 2(z + -4) + 4(z + -3)
20 + 10z + (-2 * -3 + z * -3) = 2(z + -4) + 4(z + -3)
20 + 10z + (6 + -3z) = 2(z + -4) + 4(z + -3)

Reorder the terms:
20 + 6 + 10z + -3z = 2(z + -4) + 4(z + -3)

Combine like terms: 20 + 6 = 26
26 + 10z + -3z = 2(z + -4) + 4(z + -3)

Combine like terms: 10z + -3z = 7z
26 + 7z = 2(z + -4) + 4(z + -3)

Reorder the terms:
26 + 7z = 2(-4 + z) + 4(z + -3)
26 + 7z = (-4 * 2 + z * 2) + 4(z + -3)
26 + 7z = (-8 + 2z) + 4(z + -3)

Reorder the terms:
26 + 7z = -8 + 2z + 4(-3 + z)
26 + 7z = -8 + 2z + (-3 * 4 + z * 4)
26 + 7z = -8 + 2z + (-12 + 4z)

Reorder the terms:
26 + 7z = -8 + -12 + 2z + 4z

Combine like terms: -8 + -12 = -20
26 + 7z = -20 + 2z + 4z

Combine like terms: 2z + 4z = 6z
26 + 7z = -20 + 6z

Solving
26 + 7z = -20 + 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.
26 + 7z + -6z = -20 + 6z + -6z

Combine like terms: 7z + -6z = 1z
26 + 1z = -20 + 6z + -6z

Combine like terms: 6z + -6z = 0
26 + 1z = -20 + 0
26 + 1z = -20

Add '-26' to each side of the equation.
26 + -26 + 1z = -20 + -26

Combine like terms: 26 + -26 = 0
0 + 1z = -20 + -26
1z = -20 + -26

Combine like terms: -20 + -26 = -46
1z = -46

Divide each side by '1'.
z = -46

Simplifying
z = -46