(3x+1)(x+1)=65

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Solution for (3x+1)(x+1)=65 equation: 


Simplifying
(3x + 1)(x + 1) = 65

Reorder the terms:
(1 + 3x)(x + 1) = 65

Reorder the terms:
(1 + 3x)(1 + x) = 65

Multiply (1 + 3x) * (1 + x)
(1(1 + x) + 3x * (1 + x)) = 65
((1 * 1 + x * 1) + 3x * (1 + x)) = 65
((1 + 1x) + 3x * (1 + x)) = 65
(1 + 1x + (1 * 3x + x * 3x)) = 65
(1 + 1x + (3x + 3x2)) = 65

Combine like terms: 1x + 3x = 4x
(1 + 4x + 3x2) = 65

Solving
1 + 4x + 3x2 = 65

Solving for variable 'x'.

Reorder the terms:
1 + -65 + 4x + 3x2 = 65 + -65

Combine like terms: 1 + -65 = -64
-64 + 4x + 3x2 = 65 + -65

Combine like terms: 65 + -65 = 0
-64 + 4x + 3x2 = 0

Factor a trinomial.
(-16 + -3x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-16 + -3x)' equal to zero and attempt to solve:

Simplifying
-16 + -3x = 0

Solving
-16 + -3x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -3x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -3x = 0 + 16
-3x = 0 + 16

Combine like terms: 0 + 16 = 16
-3x = 16

Divide each side by '-3'.
x = -5.333333333

Simplifying
x = -5.333333333

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-5.333333333, 4}

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