83=3(a+1)+7a

Solution for 83=3(a+1)+7a equation:

Simplifying
83 = 3(a + 1) + 7a

Reorder the terms:
83 = 3(1 + a) + 7a
83 = (1 * 3 + a * 3) + 7a
83 = (3 + 3a) + 7a

Combine like terms: 3a + 7a = 10a
83 = 3 + 10a

Solving
83 = 3 + 10a

Solving for variable 'a'.

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

Add '-10a' to each side of the equation.
83 + -10a = 3 + 10a + -10a

Combine like terms: 10a + -10a = 0
83 + -10a = 3 + 0
83 + -10a = 3

Add '-83' to each side of the equation.
83 + -83 + -10a = 3 + -83

Combine like terms: 83 + -83 = 0
0 + -10a = 3 + -83
-10a = 3 + -83

Combine like terms: 3 + -83 = -80
-10a = -80

Divide each side by '-10'.
a = 8

Simplifying
a = 8