3(x-2)(3x-7)=0

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Solution for 3(x-2)(3x-7)=0 equation:


Simplifying
3(x + -2)(3x + -7) = 0

Reorder the terms:
3(-2 + x)(3x + -7) = 0

Reorder the terms:
3(-2 + x)(-7 + 3x) = 0

Multiply (-2 + x) * (-7 + 3x)
3(-2(-7 + 3x) + x(-7 + 3x)) = 0
3((-7 * -2 + 3x * -2) + x(-7 + 3x)) = 0
3((14 + -6x) + x(-7 + 3x)) = 0
3(14 + -6x + (-7 * x + 3x * x)) = 0
3(14 + -6x + (-7x + 3x2)) = 0

Combine like terms: -6x + -7x = -13x
3(14 + -13x + 3x2) = 0
(14 * 3 + -13x * 3 + 3x2 * 3) = 0
(42 + -39x + 9x2) = 0

Solving
42 + -39x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + -13x + 3x2) = 0

Factor a trinomial.
3((2 + -1x)(7 + -3x)) = 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 + -3x)' equal to zero and attempt to solve:

Simplifying
7 + -3x = 0

Solving
7 + -3x = 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 + -3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3x = 0 + -7
-3x = 0 + -7

Combine like terms: 0 + -7 = -7
-3x = -7

Divide each side by '-3'.
x = 2.333333333

Simplifying
x = 2.333333333
Solution
x = {2, 2.333333333}

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