6(12x-42)(x-3)=0

Solution for 6(12x-42)(x-3)=0 equation:

Simplifying
6(12x + -42)(x + -3) = 0

Reorder the terms:
6(-42 + 12x)(x + -3) = 0

Reorder the terms:
6(-42 + 12x)(-3 + x) = 0

Multiply (-42 + 12x) * (-3 + x)
6(-42(-3 + x) + 12x * (-3 + x)) = 0
6((-3 * -42 + x * -42) + 12x * (-3 + x)) = 0
6((126 + -42x) + 12x * (-3 + x)) = 0
6(126 + -42x + (-3 * 12x + x * 12x)) = 0
6(126 + -42x + (-36x + 12x2)) = 0

Combine like terms: -42x + -36x = -78x
6(126 + -78x + 12x2) = 0
(126 * 6 + -78x * 6 + 12x2 * 6) = 0
(756 + -468x + 72x2) = 0

Solving
756 + -468x + 72x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '36'.
36(21 + -13x + 2x2) = 0

Factor a trinomial.
36((3 + -1x)(7 + -2x)) = 0

Ignore the factor 36.
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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {3, 3.5}