10(z-14)-4(z-2)=3(z-1)+2(z-3)

Solution for 10(z-14)-4(z-2)=3(z-1)+2(z-3) equation:

Simplifying
10(z + -14) + -4(z + -2) = 3(z + -1) + 2(z + -3)

Reorder the terms:
10(-14 + z) + -4(z + -2) = 3(z + -1) + 2(z + -3)
(-14 * 10 + z * 10) + -4(z + -2) = 3(z + -1) + 2(z + -3)
(-140 + 10z) + -4(z + -2) = 3(z + -1) + 2(z + -3)

Reorder the terms:
-140 + 10z + -4(-2 + z) = 3(z + -1) + 2(z + -3)
-140 + 10z + (-2 * -4 + z * -4) = 3(z + -1) + 2(z + -3)
-140 + 10z + (8 + -4z) = 3(z + -1) + 2(z + -3)

Reorder the terms:
-140 + 8 + 10z + -4z = 3(z + -1) + 2(z + -3)

Combine like terms: -140 + 8 = -132
-132 + 10z + -4z = 3(z + -1) + 2(z + -3)

Combine like terms: 10z + -4z = 6z
-132 + 6z = 3(z + -1) + 2(z + -3)

Reorder the terms:
-132 + 6z = 3(-1 + z) + 2(z + -3)
-132 + 6z = (-1 * 3 + z * 3) + 2(z + -3)
-132 + 6z = (-3 + 3z) + 2(z + -3)

Reorder the terms:
-132 + 6z = -3 + 3z + 2(-3 + z)
-132 + 6z = -3 + 3z + (-3 * 2 + z * 2)
-132 + 6z = -3 + 3z + (-6 + 2z)

Reorder the terms:
-132 + 6z = -3 + -6 + 3z + 2z

Combine like terms: -3 + -6 = -9
-132 + 6z = -9 + 3z + 2z

Combine like terms: 3z + 2z = 5z
-132 + 6z = -9 + 5z

Solving
-132 + 6z = -9 + 5z

Solving for variable 'z'.

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

Add '-5z' to each side of the equation.
-132 + 6z + -5z = -9 + 5z + -5z

Combine like terms: 6z + -5z = 1z
-132 + 1z = -9 + 5z + -5z

Combine like terms: 5z + -5z = 0
-132 + 1z = -9 + 0
-132 + 1z = -9

Add '132' to each side of the equation.
-132 + 132 + 1z = -9 + 132

Combine like terms: -132 + 132 = 0
0 + 1z = -9 + 132
1z = -9 + 132

Combine like terms: -9 + 132 = 123
1z = 123

Divide each side by '1'.
z = 123

Simplifying
z = 123