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

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

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

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

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

Multiply (-3 + -1x) * (1 + 4x)
(-3(1 + 4x) + -1x * (1 + 4x)) = 0
((1 * -3 + 4x * -3) + -1x * (1 + 4x)) = 0
((-3 + -12x) + -1x * (1 + 4x)) = 0
(-3 + -12x + (1 * -1x + 4x * -1x)) = 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 out the Greatest Common Factor (GCF), '-1'.
-1(3 + 13x + 4x2) = 0

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

Ignore the factor -1.
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}