3(x+1)(x+1)+13(x+1)+4=0

Solution for 3(x+1)(x+1)+13(x+1)+4=0 equation:

Simplifying
3(x + 1)(x + 1) + 13(x + 1) + 4 = 0

Reorder the terms:
3(1 + x)(x + 1) + 13(x + 1) + 4 = 0

Reorder the terms:
3(1 + x)(1 + x) + 13(x + 1) + 4 = 0

Multiply (1 + x) * (1 + x)
3(1(1 + x) + x(1 + x)) + 13(x + 1) + 4 = 0
3((1 * 1 + x * 1) + x(1 + x)) + 13(x + 1) + 4 = 0
3((1 + 1x) + x(1 + x)) + 13(x + 1) + 4 = 0
3(1 + 1x + (1 * x + x * x)) + 13(x + 1) + 4 = 0
3(1 + 1x + (1x + x2)) + 13(x + 1) + 4 = 0

Combine like terms: 1x + 1x = 2x
3(1 + 2x + x2) + 13(x + 1) + 4 = 0
(1 * 3 + 2x * 3 + x2 * 3) + 13(x + 1) + 4 = 0
(3 + 6x + 3x2) + 13(x + 1) + 4 = 0

Reorder the terms:
3 + 6x + 3x2 + 13(1 + x) + 4 = 0
3 + 6x + 3x2 + (1 * 13 + x * 13) + 4 = 0
3 + 6x + 3x2 + (13 + 13x) + 4 = 0

Reorder the terms:
3 + 13 + 4 + 6x + 13x + 3x2 = 0

Combine like terms: 3 + 13 = 16
16 + 4 + 6x + 13x + 3x2 = 0

Combine like terms: 16 + 4 = 20
20 + 6x + 13x + 3x2 = 0

Combine like terms: 6x + 13x = 19x
20 + 19x + 3x2 = 0

Solving
20 + 19x + 3x2 = 0

Solving for variable 'x'.

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

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

Simplifying
5 + x = 0

Solving
5 + x = 0

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

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

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

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

Simplifying
x = -5
Subproblem 2
Set the factor '(4 + 3x)' equal to zero and attempt to solve:

Simplifying
4 + 3x = 0

Solving
4 + 3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3x = 0 + -4

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

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

Divide each side by '3'.
x = -1.333333333

Simplifying
x = -1.333333333
Solution
x = {-5, -1.333333333}