3x^2+x+3x+1=133

Solution for 3x^2+x+3x+1=133 equation:

Simplifying
3x2 + x + 3x + 1 = 133

Reorder the terms:
1 + x + 3x + 3x2 = 133

Combine like terms: x + 3x = 4x
1 + 4x + 3x2 = 133

Solving
1 + 4x + 3x2 = 133

Solving for variable 'x'.

Reorder the terms:
1 + -133 + 4x + 3x2 = 133 + -133

Combine like terms: 1 + -133 = -132
-132 + 4x + 3x2 = 133 + -133

Combine like terms: 133 + -133 = 0
-132 + 4x + 3x2 = 0

Factor a trinomial.
(-22 + -3x)(6 + -1x) = 0

Subproblem 1
Set the factor '(-22 + -3x)' equal to zero and attempt to solve:

Simplifying
-22 + -3x = 0

Solving
-22 + -3x = 0

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

Add '22' to each side of the equation.
-22 + 22 + -3x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -3x = 0 + 22
-3x = 0 + 22

Combine like terms: 0 + 22 = 22
-3x = 22

Divide each side by '-3'.
x = -7.333333333

Simplifying
x = -7.333333333
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-7.333333333, 6}