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

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


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

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

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

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

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

Solving
65 = 1 + 4x + 3x2

Solving for variable 'x'.

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

Reorder the terms:
64 + -4x + -3x2 = 1 + -1 + 4x + -4x + 3x2 + -3x2

Combine like terms: 1 + -1 = 0
64 + -4x + -3x2 = 0 + 4x + -4x + 3x2 + -3x2
64 + -4x + -3x2 = 4x + -4x + 3x2 + -3x2

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

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

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


Subproblem 1
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

Subproblem 2
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
Solution
x = {4, -5.333333333}

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