(3x-27)(2-18x)=0

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Solution for (3x-27)(2-18x)=0 equation:


Simplifying
(3x + -27)(2 + -18x) = 0

Reorder the terms:
(-27 + 3x)(2 + -18x) = 0

Multiply (-27 + 3x) * (2 + -18x)
(-27(2 + -18x) + 3x * (2 + -18x)) = 0
((2 * -27 + -18x * -27) + 3x * (2 + -18x)) = 0
((-54 + 486x) + 3x * (2 + -18x)) = 0
(-54 + 486x + (2 * 3x + -18x * 3x)) = 0
(-54 + 486x + (6x + -54x2)) = 0

Combine like terms: 486x + 6x = 492x
(-54 + 492x + -54x2) = 0

Solving
-54 + 492x + -54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-9 + 82x + -9x2) = 0

Factor a trinomial.
6((-9 + x)(1 + -9x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-9 + x)' equal to zero and attempt to solve: Simplifying -9 + x = 0 Solving -9 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x = 0 + 9 x = 0 + 9 Combine like terms: 0 + 9 = 9 x = 9 Simplifying x = 9

Subproblem 2

Set the factor '(1 + -9x)' equal to zero and attempt to solve: Simplifying 1 + -9x = 0 Solving 1 + -9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -9x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -9x = 0 + -1 -9x = 0 + -1 Combine like terms: 0 + -1 = -1 -9x = -1 Divide each side by '-9'. x = 0.1111111111 Simplifying x = 0.1111111111

Solution

x = {9, 0.1111111111}

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