16x^2-1+(4x+1)(3+x)=0

Solution for 16x^2-1+(4x+1)(3+x)=0 equation:

Simplifying
16x2 + -1 + (4x + 1)(3 + x) = 0

Reorder the terms:
16x2 + -1 + (1 + 4x)(3 + x) = 0

Multiply (1 + 4x) * (3 + x)
16x2 + -1 + (1(3 + x) + 4x * (3 + x)) = 0
16x2 + -1 + ((3 * 1 + x * 1) + 4x * (3 + x)) = 0
16x2 + -1 + ((3 + 1x) + 4x * (3 + x)) = 0
16x2 + -1 + (3 + 1x + (3 * 4x + x * 4x)) = 0
16x2 + -1 + (3 + 1x + (12x + 4x2)) = 0

Combine like terms: 1x + 12x = 13x
16x2 + -1 + (3 + 13x + 4x2) = 0

Reorder the terms:
-1 + 3 + 13x + 16x2 + 4x2 = 0

Combine like terms: -1 + 3 = 2
2 + 13x + 16x2 + 4x2 = 0

Combine like terms: 16x2 + 4x2 = 20x2
2 + 13x + 20x2 = 0

Solving
2 + 13x + 20x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2 + 5x)(1 + 4x) = 0

Subproblem 1
Set the factor '(2 + 5x)' equal to zero and attempt to solve:

Simplifying
2 + 5x = 0

Solving
2 + 5x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2

Combine like terms: 0 + -2 = -2
5x = -2

Divide each side by '5'.
x = -0.4

Simplifying
x = -0.4
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 = {-0.4, -0.25}