6x^2-144x+864-5400=0

Solution for 6x^2-144x+864-5400=0 equation:

Simplifying
6x2 + -144x + 864 + -5400 = 0

Reorder the terms:
864 + -5400 + -144x + 6x2 = 0

Combine like terms: 864 + -5400 = -4536
-4536 + -144x + 6x2 = 0

Solving
-4536 + -144x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-756 + -24x + x2) = 0

Factor a trinomial.
6((-18 + -1x)(42 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-18 + -1x)' equal to zero and attempt to solve:

Simplifying
-18 + -1x = 0

Solving
-18 + -1x = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1x = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1x = 0 + 18
-1x = 0 + 18

Combine like terms: 0 + 18 = 18
-1x = 18

Divide each side by '-1'.
x = -18

Simplifying
x = -18
Subproblem 2
Set the factor '(42 + -1x)' equal to zero and attempt to solve:

Simplifying
42 + -1x = 0

Solving
42 + -1x = 0

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

Add '-42' to each side of the equation.
42 + -42 + -1x = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -1x = 0 + -42
-1x = 0 + -42

Combine like terms: 0 + -42 = -42
-1x = -42

Divide each side by '-1'.
x = 42

Simplifying
x = 42
Solution
x = {-18, 42}