(4x+1)(x+6)=0

Solution for (4x+1)(x+6)=0 equation:

Simplifying
(4x + 1)(x + 6) = 0

Reorder the terms:
(1 + 4x)(x + 6) = 0

Reorder the terms:
(1 + 4x)(6 + x) = 0

Multiply (1 + 4x) * (6 + x)
(1(6 + x) + 4x * (6 + x)) = 0
((6 * 1 + x * 1) + 4x * (6 + x)) = 0
((6 + 1x) + 4x * (6 + x)) = 0
(6 + 1x + (6 * 4x + x * 4x)) = 0
(6 + 1x + (24x + 4x2)) = 0

Combine like terms: 1x + 24x = 25x
(6 + 25x + 4x2) = 0

Solving
6 + 25x + 4x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
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 = {-6, -0.25}