(3x-6)(x-7)=0

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Solution for (3x-6)(x-7)=0 equation: 


Simplifying
(3x + -6)(x + -7) = 0

Reorder the terms:
(-6 + 3x)(x + -7) = 0

Reorder the terms:
(-6 + 3x)(-7 + x) = 0

Multiply (-6 + 3x) * (-7 + x)
(-6(-7 + x) + 3x * (-7 + x)) = 0
((-7 * -6 + x * -6) + 3x * (-7 + x)) = 0
((42 + -6x) + 3x * (-7 + x)) = 0
(42 + -6x + (-7 * 3x + x * 3x)) = 0
(42 + -6x + (-21x + 3x2)) = 0

Combine like terms: -6x + -21x = -27x
(42 + -27x + 3x2) = 0

Solving
42 + -27x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + -9x + x2) = 0

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

Ignore the factor 3.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 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 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {2, 7}

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