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

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


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

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

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

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

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

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

Combine like terms: 1 + 65 = 66
1 + 4x + 3x2 = 66 + x + x

Combine like terms: x + x = 2x
1 + 4x + 3x2 = 66 + 2x

Solving
1 + 4x + 3x2 = 66 + 2x

Solving for variable 'x'.

Reorder the terms:
1 + -66 + 4x + -2x + 3x2 = 66 + 2x + -66 + -2x

Combine like terms: 1 + -66 = -65
-65 + 4x + -2x + 3x2 = 66 + 2x + -66 + -2x

Combine like terms: 4x + -2x = 2x
-65 + 2x + 3x2 = 66 + 2x + -66 + -2x

Reorder the terms:
-65 + 2x + 3x2 = 66 + -66 + 2x + -2x

Combine like terms: 66 + -66 = 0
-65 + 2x + 3x2 = 0 + 2x + -2x
-65 + 2x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-65 + 2x + 3x2 = 0

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


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

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
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
Solution
x = {-5, 4.333333333}

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