x(x+13)=4x(x-1)-6

Solution for x(x+13)=4x(x-1)-6 equation:

Simplifying
x(x + 13) = 4x(x + -1) + -6

Reorder the terms:
x(13 + x) = 4x(x + -1) + -6
(13 * x + x * x) = 4x(x + -1) + -6
(13x + x2) = 4x(x + -1) + -6

Reorder the terms:
13x + x2 = 4x(-1 + x) + -6
13x + x2 = (-1 * 4x + x * 4x) + -6
13x + x2 = (-4x + 4x2) + -6

Reorder the terms:
13x + x2 = -6 + -4x + 4x2

Solving
13x + x2 = -6 + -4x + 4x2

Solving for variable 'x'.

Reorder the terms:
6 + 13x + 4x + x2 + -4x2 = -6 + -4x + 4x2 + 6 + 4x + -4x2

Combine like terms: 13x + 4x = 17x
6 + 17x + x2 + -4x2 = -6 + -4x + 4x2 + 6 + 4x + -4x2

Combine like terms: x2 + -4x2 = -3x2
6 + 17x + -3x2 = -6 + -4x + 4x2 + 6 + 4x + -4x2

Reorder the terms:
6 + 17x + -3x2 = -6 + 6 + -4x + 4x + 4x2 + -4x2

Combine like terms: -6 + 6 = 0
6 + 17x + -3x2 = 0 + -4x + 4x + 4x2 + -4x2
6 + 17x + -3x2 = -4x + 4x + 4x2 + -4x2

Combine like terms: -4x + 4x = 0
6 + 17x + -3x2 = 0 + 4x2 + -4x2
6 + 17x + -3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
6 + 17x + -3x2 = 0

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

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

Simplifying
1 + 3x = 0

Solving
1 + 3x = 0

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

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

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

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

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {6, -0.3333333333}