x=(3x+1)(x-10)

Solution for x=(3x+1)(x-10) equation:

Simplifying
x = (3x + 1)(x + -10)

Reorder the terms:
x = (1 + 3x)(x + -10)

Reorder the terms:
x = (1 + 3x)(-10 + x)

Multiply (1 + 3x) * (-10 + x)
x = (1(-10 + x) + 3x * (-10 + x))
x = ((-10 * 1 + x * 1) + 3x * (-10 + x))
x = ((-10 + 1x) + 3x * (-10 + x))
x = (-10 + 1x + (-10 * 3x + x * 3x))
x = (-10 + 1x + (-30x + 3x2))

Combine like terms: 1x + -30x = -29x
x = (-10 + -29x + 3x2)

Solving
x = -10 + -29x + 3x2

Solving for variable 'x'.

Reorder the terms:
10 + x + 29x + -3x2 = -10 + -29x + 3x2 + 10 + 29x + -3x2

Combine like terms: x + 29x = 30x
10 + 30x + -3x2 = -10 + -29x + 3x2 + 10 + 29x + -3x2

Reorder the terms:
10 + 30x + -3x2 = -10 + 10 + -29x + 29x + 3x2 + -3x2

Combine like terms: -10 + 10 = 0
10 + 30x + -3x2 = 0 + -29x + 29x + 3x2 + -3x2
10 + 30x + -3x2 = -29x + 29x + 3x2 + -3x2

Combine like terms: -29x + 29x = 0
10 + 30x + -3x2 = 0 + 3x2 + -3x2
10 + 30x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
10 + 30x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-3.333333333 + -10x + x2 = 0

Move the constant term to the right:

Add '3.333333333' to each side of the equation.
-3.333333333 + -10x + 3.333333333 + x2 = 0 + 3.333333333

Reorder the terms:
-3.333333333 + 3.333333333 + -10x + x2 = 0 + 3.333333333

Combine like terms: -3.333333333 + 3.333333333 = 0.000000000
0.000000000 + -10x + x2 = 0 + 3.333333333
-10x + x2 = 0 + 3.333333333

Combine like terms: 0 + 3.333333333 = 3.333333333
-10x + x2 = 3.333333333

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 3.333333333 + 25

Reorder the terms:
25 + -10x + x2 = 3.333333333 + 25

Combine like terms: 3.333333333 + 25 = 28.333333333
25 + -10x + x2 = 28.333333333

Factor a perfect square on the left side:
(x + -5)(x + -5) = 28.333333333

Calculate the square root of the right side: 5.322906474

Break this problem into two subproblems by setting 
(x + -5) equal to 5.322906474 and -5.322906474.

Subproblem 1
x + -5 = 5.322906474

Simplifying
x + -5 = 5.322906474

Reorder the terms:
-5 + x = 5.322906474

Solving
-5 + x = 5.322906474

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 5.322906474 + 5

Combine like terms: -5 + 5 = 0
0 + x = 5.322906474 + 5
x = 5.322906474 + 5

Combine like terms: 5.322906474 + 5 = 10.322906474
x = 10.322906474

Simplifying
x = 10.322906474

Subproblem 2
x + -5 = -5.322906474

Simplifying
x + -5 = -5.322906474

Reorder the terms:
-5 + x = -5.322906474

Solving
-5 + x = -5.322906474

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -5.322906474 + 5

Combine like terms: -5 + 5 = 0
0 + x = -5.322906474 + 5
x = -5.322906474 + 5

Combine like terms: -5.322906474 + 5 = -0.322906474
x = -0.322906474

Simplifying
x = -0.322906474

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.322906474, -0.322906474}