(6-2x)(13-2x)(x)=0

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Solution for (6-2x)(13-2x)(x)=0 equation: 


Simplifying
(6 + -2x)(13 + -2x)(x) = 0

Reorder the terms for easier multiplication:
x(6 + -2x)(13 + -2x) = 0

Multiply (6 + -2x) * (13 + -2x)
x(6(13 + -2x) + -2x * (13 + -2x)) = 0
x((13 * 6 + -2x * 6) + -2x * (13 + -2x)) = 0
x((78 + -12x) + -2x * (13 + -2x)) = 0
x(78 + -12x + (13 * -2x + -2x * -2x)) = 0
x(78 + -12x + (-26x + 4x2)) = 0

Combine like terms: -12x + -26x = -38x
x(78 + -38x + 4x2) = 0
(78 * x + -38x * x + 4x2 * x) = 0
(78x + -38x2 + 4x3) = 0

Solving
78x + -38x2 + 4x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(39 + -19x + 2x2) = 0

Factor a trinomial.
2x((3 + -1x)(13 + -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 '(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 3
Set the factor '(13 + -2x)' equal to zero and attempt to solve:

Simplifying
13 + -2x = 0

Solving
13 + -2x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2x = 0 + -13
-2x = 0 + -13

Combine like terms: 0 + -13 = -13
-2x = -13

Divide each side by '-2'.
x = 6.5

Simplifying
x = 6.5
Solution
x = {0, 3, 6.5}

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