x(x+6)=8x+3

Solution for x(x+6)=8x+3 equation:

Simplifying
x(x + 6) = 8x + 3

Reorder the terms:
x(6 + x) = 8x + 3
(6 * x + x * x) = 8x + 3
(6x + x2) = 8x + 3

Reorder the terms:
6x + x2 = 3 + 8x

Solving
6x + x2 = 3 + 8x

Solving for variable 'x'.

Reorder the terms:
-3 + 6x + -8x + x2 = 3 + 8x + -3 + -8x

Combine like terms: 6x + -8x = -2x
-3 + -2x + x2 = 3 + 8x + -3 + -8x

Reorder the terms:
-3 + -2x + x2 = 3 + -3 + 8x + -8x

Combine like terms: 3 + -3 = 0
-3 + -2x + x2 = 0 + 8x + -8x
-3 + -2x + x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
-3 + -2x + x2 = 0

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

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
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 = {-1, 3}