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

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


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

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

Combine like terms: 1 + 4 = 5
(13 + 3x)(5)(x + 1) = 0

Reorder the terms:
(13 + 3x) * 5(1 + x) = 0

Reorder the terms for easier multiplication:
5(13 + 3x)(1 + x) = 0

Multiply (13 + 3x) * (1 + x)
5(13(1 + x) + 3x * (1 + x)) = 0
5((1 * 13 + x * 13) + 3x * (1 + x)) = 0
5((13 + 13x) + 3x * (1 + x)) = 0
5(13 + 13x + (1 * 3x + x * 3x)) = 0
5(13 + 13x + (3x + 3x2)) = 0

Combine like terms: 13x + 3x = 16x
5(13 + 16x + 3x2) = 0
(13 * 5 + 16x * 5 + 3x2 * 5) = 0
(65 + 80x + 15x2) = 0

Solving
65 + 80x + 15x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(13 + 16x + 3x2) = 0

Factor a trinomial.
5((13 + 3x)(1 + x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(13 + 3x)' equal to zero and attempt to solve:

Simplifying
13 + 3x = 0

Solving
13 + 3x = 0

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

Add '-13' to each side of the equation.
13 + -13 + 3x = 0 + -13

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

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

Divide each side by '3'.
x = -4.333333333

Simplifying
x = -4.333333333

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

Simplifying
1 + x = 0

Solving
1 + x = 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 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-4.333333333, -1}

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