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

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

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

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

Reorder the terms:
40 + 10z + -4(-2 + z) = 3(z + -1) + s(z + -3)
40 + 10z + (-2 * -4 + z * -4) = 3(z + -1) + s(z + -3)
40 + 10z + (8 + -4z) = 3(z + -1) + s(z + -3)

Reorder the terms:
40 + 8 + 10z + -4z = 3(z + -1) + s(z + -3)

Combine like terms: 40 + 8 = 48
48 + 10z + -4z = 3(z + -1) + s(z + -3)

Combine like terms: 10z + -4z = 6z
48 + 6z = 3(z + -1) + s(z + -3)

Reorder the terms:
48 + 6z = 3(-1 + z) + s(z + -3)
48 + 6z = (-1 * 3 + z * 3) + s(z + -3)
48 + 6z = (-3 + 3z) + s(z + -3)

Reorder the terms:
48 + 6z = -3 + 3z + s(-3 + z)
48 + 6z = -3 + 3z + (-3 * s + z * s)
48 + 6z = -3 + 3z + (-3s + sz)

Reorder the terms:
48 + 6z = -3 + -3s + sz + 3z

Solving
48 + 6z = -3 + -3s + sz + 3z

Solving for variable 'z'.

Move all terms containing z to the left, all other terms to the right.

Add '-1sz' to each side of the equation.
48 + -1sz + 6z = -3 + -3s + sz + -1sz + 3z

Combine like terms: sz + -1sz = 0
48 + -1sz + 6z = -3 + -3s + 0 + 3z
48 + -1sz + 6z = -3 + -3s + 3z

Add '-3z' to each side of the equation.
48 + -1sz + 6z + -3z = -3 + -3s + 3z + -3z

Combine like terms: 6z + -3z = 3z
48 + -1sz + 3z = -3 + -3s + 3z + -3z

Combine like terms: 3z + -3z = 0
48 + -1sz + 3z = -3 + -3s + 0
48 + -1sz + 3z = -3 + -3s

Add '-48' to each side of the equation.
48 + -1sz + -48 + 3z = -3 + -48 + -3s

Reorder the terms:
48 + -48 + -1sz + 3z = -3 + -48 + -3s

Combine like terms: 48 + -48 = 0
0 + -1sz + 3z = -3 + -48 + -3s
-1sz + 3z = -3 + -48 + -3s

Combine like terms: -3 + -48 = -51
-1sz + 3z = -51 + -3s

Reorder the terms:
51 + 3s + -1sz + 3z = -51 + -3s + 51 + 3s

Reorder the terms:
51 + 3s + -1sz + 3z = -51 + 51 + -3s + 3s

Combine like terms: -51 + 51 = 0
51 + 3s + -1sz + 3z = 0 + -3s + 3s
51 + 3s + -1sz + 3z = -3s + 3s

Combine like terms: -3s + 3s = 0
51 + 3s + -1sz + 3z = 0

The solution to this equation could not be determined.