x(12-2x)(21-2x)=0

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Solution for x(12-2x)(21-2x)=0 equation: 


Simplifying
x(12 + -2x)(21 + -2x) = 0

Multiply (12 + -2x) * (21 + -2x)
x(12(21 + -2x) + -2x * (21 + -2x)) = 0
x((21 * 12 + -2x * 12) + -2x * (21 + -2x)) = 0
x((252 + -24x) + -2x * (21 + -2x)) = 0
x(252 + -24x + (21 * -2x + -2x * -2x)) = 0
x(252 + -24x + (-42x + 4x2)) = 0

Combine like terms: -24x + -42x = -66x
x(252 + -66x + 4x2) = 0
(252 * x + -66x * x + 4x2 * x) = 0
(252x + -66x2 + 4x3) = 0

Solving
252x + -66x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(126 + -33x + 2x2) = 0

Factor a trinomial.
2x((6 + -1x)(21 + -2x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 3
Set the factor '(21 + -2x)' equal to zero and attempt to solve:

Simplifying
21 + -2x = 0

Solving
21 + -2x = 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 + -2x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + -2x = 0 + -21
-2x = 0 + -21

Combine like terms: 0 + -21 = -21
-2x = -21

Divide each side by '-2'.
x = 10.5

Simplifying
x = 10.5
Solution
x = {0, 6, 10.5}

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