(3x-18)(x-3)=0

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Solution for (3x-18)(x-3)=0 equation:


Simplifying
(3x + -18)(x + -3) = 0

Reorder the terms:
(-18 + 3x)(x + -3) = 0

Reorder the terms:
(-18 + 3x)(-3 + x) = 0

Multiply (-18 + 3x) * (-3 + x)
(-18(-3 + x) + 3x * (-3 + x)) = 0
((-3 * -18 + x * -18) + 3x * (-3 + x)) = 0
((54 + -18x) + 3x * (-3 + x)) = 0
(54 + -18x + (-3 * 3x + x * 3x)) = 0
(54 + -18x + (-9x + 3x2)) = 0

Combine like terms: -18x + -9x = -27x
(54 + -27x + 3x2) = 0

Solving
54 + -27x + 3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -9x + x2) = 0

Factor a trinomial.
3((3 + -1x)(6 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

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 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

Solution

x = {3, 6}

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