(X-2)(X+6)=8X

Solution for (X-2)(X+6)=8X equation:

Simplifying
(X + -2)(X + 6) = 8X

Reorder the terms:
(-2 + X)(X + 6) = 8X

Reorder the terms:
(-2 + X)(6 + X) = 8X

Multiply (-2 + X) * (6 + X)
(-2(6 + X) + X(6 + X)) = 8X
((6 * -2 + X * -2) + X(6 + X)) = 8X
((-12 + -2X) + X(6 + X)) = 8X
(-12 + -2X + (6 * X + X * X)) = 8X
(-12 + -2X + (6X + X2)) = 8X

Combine like terms: -2X + 6X = 4X
(-12 + 4X + X2) = 8X

Solving
-12 + 4X + X2 = 8X

Solving for variable 'X'.

Reorder the terms:
-12 + 4X + -8X + X2 = 8X + -8X

Combine like terms: 4X + -8X = -4X
-12 + -4X + X2 = 8X + -8X

Combine like terms: 8X + -8X = 0
-12 + -4X + X2 = 0

Factor a trinomial.
(-2 + -1X)(6 + -1X) = 0

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

Simplifying
-2 + -1X = 0

Solving
-2 + -1X = 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 + -1X = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1X = 0 + 2
-1X = 0 + 2

Combine like terms: 0 + 2 = 2
-1X = 2

Divide each side by '-1'.
X = -2

Simplifying
X = -2
Subproblem 2
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
Solution
X = {-2, 6}