(x-6)(x-4)(3)=765

Solution for (x-6)(x-4)(3)=765 equation:

Simplifying
(x + -6)(x + -4)(3) = 765

Reorder the terms:
(-6 + x)(x + -4)(3) = 765

Reorder the terms:
(-6 + x)(-4 + x)(3) = 765

Reorder the terms for easier multiplication:
3(-6 + x)(-4 + x) = 765

Multiply (-6 + x) * (-4 + x)
3(-6(-4 + x) + x(-4 + x)) = 765
3((-4 * -6 + x * -6) + x(-4 + x)) = 765
3((24 + -6x) + x(-4 + x)) = 765
3(24 + -6x + (-4 * x + x * x)) = 765
3(24 + -6x + (-4x + x2)) = 765

Combine like terms: -6x + -4x = -10x
3(24 + -10x + x2) = 765
(24 * 3 + -10x * 3 + x2 * 3) = 765
(72 + -30x + 3x2) = 765

Solving
72 + -30x + 3x2 = 765

Solving for variable 'x'.

Reorder the terms:
72 + -765 + -30x + 3x2 = 765 + -765

Combine like terms: 72 + -765 = -693
-693 + -30x + 3x2 = 765 + -765

Combine like terms: 765 + -765 = 0
-693 + -30x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-231 + -10x + x2) = 0

Factor a trinomial.
3((-11 + -1x)(21 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve:

Simplifying
-11 + -1x = 0

Solving
-11 + -1x = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1x = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1x = 0 + 11
-1x = 0 + 11

Combine like terms: 0 + 11 = 11
-1x = 11

Divide each side by '-1'.
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(21 + -1x)' equal to zero and attempt to solve:

Simplifying
21 + -1x = 0

Solving
21 + -1x = 0

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

Add '-21' to each side of the equation.
21 + -21 + -1x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -1x = 0 + -21
-1x = 0 + -21

Combine like terms: 0 + -21 = -21
-1x = -21

Divide each side by '-1'.
x = 21

Simplifying
x = 21
Solution
x = {-11, 21}