(x+1)(3x+1)=5

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Solution for (x+1)(3x+1)=5 equation: 


Simplifying
(x + 1)(3x + 1) = 5

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

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

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

Combine like terms: 3x + 1x = 4x
(1 + 4x + 3x2) = 5

Solving
1 + 4x + 3x2 = 5

Solving for variable 'x'.

Reorder the terms:
1 + -5 + 4x + 3x2 = 5 + -5

Combine like terms: 1 + -5 = -4
-4 + 4x + 3x2 = 5 + -5

Combine like terms: 5 + -5 = 0
-4 + 4x + 3x2 = 0

Factor a trinomial.
(-2 + -1x)(2 + -3x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 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 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-2, 0.6666666667}

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