42=7v(z-3)

Solution for 42=7v(z-3) equation:

Simplifying
42 = 7v(z + -3)

Reorder the terms:
42 = 7v(-3 + z)
42 = (-3 * 7v + z * 7v)
42 = (-21v + 7vz)

Solving
42 = -21v + 7vz

Solving for variable 'v'.

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

Add '21v' to each side of the equation.
42 + 21v = -21v + 21v + 7vz

Combine like terms: -21v + 21v = 0
42 + 21v = 0 + 7vz
42 + 21v = 7vz

Add '-7vz' to each side of the equation.
42 + 21v + -7vz = 7vz + -7vz

Combine like terms: 7vz + -7vz = 0
42 + 21v + -7vz = 0

Add '-42' to each side of the equation.
42 + 21v + -42 + -7vz = 0 + -42

Reorder the terms:
42 + -42 + 21v + -7vz = 0 + -42

Combine like terms: 42 + -42 = 0
0 + 21v + -7vz = 0 + -42
21v + -7vz = 0 + -42

Combine like terms: 0 + -42 = -42
21v + -7vz = -42

Reorder the terms:
42 + 21v + -7vz = -42 + 42

Combine like terms: -42 + 42 = 0
42 + 21v + -7vz = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(6 + 3v + -1vz) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(6 + 3v + -1vz)' equal to zero and attempt to solve:

Simplifying
6 + 3v + -1vz = 0

Solving
6 + 3v + -1vz = 0

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

Add '-6' to each side of the equation.
6 + 3v + -6 + -1vz = 0 + -6

Reorder the terms:
6 + -6 + 3v + -1vz = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 3v + -1vz = 0 + -6
3v + -1vz = 0 + -6

Combine like terms: 0 + -6 = -6
3v + -1vz = -6

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.