x(4x+13)=-3

Solution for x(4x+13)=-3 equation:

Simplifying
x(4x + 13) = -3

Reorder the terms:
x(13 + 4x) = -3
(13 * x + 4x * x) = -3
(13x + 4x2) = -3

Solving
13x + 4x2 = -3

Solving for variable 'x'.

Reorder the terms:
3 + 13x + 4x2 = -3 + 3

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

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}