(3x+1)*(x)=30

Solution for (3x+1)*(x)=30 equation:

Simplifying
(3x + 1)(x) = 30

Reorder the terms:
(1 + 3x)(x) = 30

Reorder the terms for easier multiplication:
x(1 + 3x) = 30
(1 * x + 3x * x) = 30
(1x + 3x2) = 30

Solving
1x + 3x2 = 30

Solving for variable 'x'.

Reorder the terms:
-30 + 1x + 3x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 1x + 3x2 = 0

Factor a trinomial.
(-10 + -3x)(3 + -1x) = 0

Subproblem 1
Set the factor '(-10 + -3x)' equal to zero and attempt to solve:

Simplifying
-10 + -3x = 0

Solving
-10 + -3x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -3x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -3x = 0 + 10
-3x = 0 + 10

Combine like terms: 0 + 10 = 10
-3x = 10

Divide each side by '-3'.
x = -3.333333333

Simplifying
x = -3.333333333
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-3.333333333, 3}