3(4x+1)+x(4x+1)=0

Solution for 3(4x+1)+x(4x+1)=0 equation:

Simplifying
3(4x + 1) + x(4x + 1) = 0

Reorder the terms:
3(1 + 4x) + x(4x + 1) = 0
(1 * 3 + 4x * 3) + x(4x + 1) = 0
(3 + 12x) + x(4x + 1) = 0

Reorder the terms:
3 + 12x + x(1 + 4x) = 0
3 + 12x + (1 * x + 4x * x) = 0
3 + 12x + (1x + 4x2) = 0

Combine like terms: 12x + 1x = 13x
3 + 13x + 4x2 = 0

Solving
3 + 13x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + x)(1 + 4x) = 0

Subproblem 1
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {-3, -0.25}