(2x+3)(4x+1)=0

Solution for (2x+3)(4x+1)=0 equation:

Simplifying
(2x + 3)(4x + 1) = 0

Reorder the terms:
(3 + 2x)(4x + 1) = 0

Reorder the terms:
(3 + 2x)(1 + 4x) = 0

Multiply (3 + 2x) * (1 + 4x)
(3(1 + 4x) + 2x * (1 + 4x)) = 0
((1 * 3 + 4x * 3) + 2x * (1 + 4x)) = 0
((3 + 12x) + 2x * (1 + 4x)) = 0
(3 + 12x + (1 * 2x + 4x * 2x)) = 0
(3 + 12x + (2x + 8x2)) = 0

Combine like terms: 12x + 2x = 14x
(3 + 14x + 8x2) = 0

Solving
3 + 14x + 8x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + 2x)(1 + 4x) = 0

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, -0.25}