33=3(1+3v)+v

Solution for 33=3(1+3v)+v equation:

Simplifying
33 = 3(1 + 3v) + v
33 = (1 * 3 + 3v * 3) + v
33 = (3 + 9v) + v

Combine like terms: 9v + v = 10v
33 = 3 + 10v

Solving
33 = 3 + 10v

Solving for variable 'v'.

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

Add '-10v' to each side of the equation.
33 + -10v = 3 + 10v + -10v

Combine like terms: 10v + -10v = 0
33 + -10v = 3 + 0
33 + -10v = 3

Add '-33' to each side of the equation.
33 + -33 + -10v = 3 + -33

Combine like terms: 33 + -33 = 0
0 + -10v = 3 + -33
-10v = 3 + -33

Combine like terms: 3 + -33 = -30
-10v = -30

Divide each side by '-10'.
v = 3

Simplifying
v = 3