x(3x+13)=10

Solution for x(3x+13)=10 equation:

Simplifying
x(3x + 13) = 10

Reorder the terms:
x(13 + 3x) = 10
(13 * x + 3x * x) = 10
(13x + 3x2) = 10

Solving
13x + 3x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + 13x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 13x + 3x2 = 0

Factor a trinomial.
(-5 + -1x)(2 + -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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3x = 0 + -2

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {-5, 0.6666666667}