2x(x-3)=8(x-3)

Solution for 2x(x-3)=8(x-3) equation:

Simplifying
2x(x + -3) = 8(x + -3)

Reorder the terms:
2x(-3 + x) = 8(x + -3)
(-3 * 2x + x * 2x) = 8(x + -3)
(-6x + 2x2) = 8(x + -3)

Reorder the terms:
-6x + 2x2 = 8(-3 + x)
-6x + 2x2 = (-3 * 8 + x * 8)
-6x + 2x2 = (-24 + 8x)

Solving
-6x + 2x2 = -24 + 8x

Solving for variable 'x'.

Reorder the terms:
24 + -6x + -8x + 2x2 = -24 + 8x + 24 + -8x

Combine like terms: -6x + -8x = -14x
24 + -14x + 2x2 = -24 + 8x + 24 + -8x

Reorder the terms:
24 + -14x + 2x2 = -24 + 24 + 8x + -8x

Combine like terms: -24 + 24 = 0
24 + -14x + 2x2 = 0 + 8x + -8x
24 + -14x + 2x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
24 + -14x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + -7x + x2) = 0

Factor a trinomial.
2((3 + -1x)(4 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {3, 4}