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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