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

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

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

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

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

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

Combine like terms: 10 + 6 = 16
16 + 10z + -2z = 4(z + -3) + 3(z + -3)

Combine like terms: 10z + -2z = 8z
16 + 8z = 4(z + -3) + 3(z + -3)

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

Reorder the terms:
16 + 8z = -12 + 4z + 3(-3 + z)
16 + 8z = -12 + 4z + (-3 * 3 + z * 3)
16 + 8z = -12 + 4z + (-9 + 3z)

Reorder the terms:
16 + 8z = -12 + -9 + 4z + 3z

Combine like terms: -12 + -9 = -21
16 + 8z = -21 + 4z + 3z

Combine like terms: 4z + 3z = 7z
16 + 8z = -21 + 7z

Solving
16 + 8z = -21 + 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.
16 + 8z + -7z = -21 + 7z + -7z

Combine like terms: 8z + -7z = 1z
16 + 1z = -21 + 7z + -7z

Combine like terms: 7z + -7z = 0
16 + 1z = -21 + 0
16 + 1z = -21

Add '-16' to each side of the equation.
16 + -16 + 1z = -21 + -16

Combine like terms: 16 + -16 = 0
0 + 1z = -21 + -16
1z = -21 + -16

Combine like terms: -21 + -16 = -37
1z = -37

Divide each side by '1'.
z = -37

Simplifying
z = -37