(x-4)x(-6)=3(8-2x)

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Solution for (x-4)x(-6)=3(8-2x) equation: 


Simplifying
(x + -4) * x(-6) = 3(8 + -2x)

Reorder the terms:
(-4 + x) * x(-6) = 3(8 + -2x)

Reorder the terms for easier multiplication:
-6x(-4 + x) = 3(8 + -2x)
(-4 * -6x + x * -6x) = 3(8 + -2x)
(24x + -6x2) = 3(8 + -2x)
24x + -6x2 = (8 * 3 + -2x * 3)
24x + -6x2 = (24 + -6x)

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

Solving for variable 'x'.

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

Combine like terms: 24x + 6x = 30x
-24 + 30x + -6x2 = 24 + -6x + -24 + 6x

Reorder the terms:
-24 + 30x + -6x2 = 24 + -24 + -6x + 6x

Combine like terms: 24 + -24 = 0
-24 + 30x + -6x2 = 0 + -6x + 6x
-24 + 30x + -6x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-24 + 30x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + 5x + -1x2) = 0

Factor a trinomial.
6((-4 + x)(1 + -1x)) = 0

Ignore the factor 6.

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

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

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

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

Simplifying
x = 4

Subproblem 2
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
Solution
x = {4, 1}

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