3(4a+1)-(4a+1)=-43-(3a-1)

Solution for 3(4a+1)-(4a+1)=-43-(3a-1) equation:

Simplifying
3(4a + 1) + -1(4a + 1) = -43 + -1(3a + -1)

Reorder the terms:
3(1 + 4a) + -1(4a + 1) = -43 + -1(3a + -1)
(1 * 3 + 4a * 3) + -1(4a + 1) = -43 + -1(3a + -1)
(3 + 12a) + -1(4a + 1) = -43 + -1(3a + -1)

Reorder the terms:
3 + 12a + -1(1 + 4a) = -43 + -1(3a + -1)
3 + 12a + (1 * -1 + 4a * -1) = -43 + -1(3a + -1)
3 + 12a + (-1 + -4a) = -43 + -1(3a + -1)

Reorder the terms:
3 + -1 + 12a + -4a = -43 + -1(3a + -1)

Combine like terms: 3 + -1 = 2
2 + 12a + -4a = -43 + -1(3a + -1)

Combine like terms: 12a + -4a = 8a
2 + 8a = -43 + -1(3a + -1)

Reorder the terms:
2 + 8a = -43 + -1(-1 + 3a)
2 + 8a = -43 + (-1 * -1 + 3a * -1)
2 + 8a = -43 + (1 + -3a)

Combine like terms: -43 + 1 = -42
2 + 8a = -42 + -3a

Solving
2 + 8a = -42 + -3a

Solving for variable 'a'.

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

Add '3a' to each side of the equation.
2 + 8a + 3a = -42 + -3a + 3a

Combine like terms: 8a + 3a = 11a
2 + 11a = -42 + -3a + 3a

Combine like terms: -3a + 3a = 0
2 + 11a = -42 + 0
2 + 11a = -42

Add '-2' to each side of the equation.
2 + -2 + 11a = -42 + -2

Combine like terms: 2 + -2 = 0
0 + 11a = -42 + -2
11a = -42 + -2

Combine like terms: -42 + -2 = -44
11a = -44

Divide each side by '11'.
a = -4

Simplifying
a = -4