0=4x^2+13x+3

Solution for 0=4x^2+13x+3 equation:

Simplifying
0 = 4x2 + 13x + 3

Reorder the terms:
0 = 3 + 13x + 4x2

Solving
0 = 3 + 13x + 4x2

Solving for variable 'x'.

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

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

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

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

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

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}