(5x-15)(6x-18)=0

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Solution for (5x-15)(6x-18)=0 equation:


Simplifying
(5x + -15)(6x + -18) = 0

Reorder the terms:
(-15 + 5x)(6x + -18) = 0

Reorder the terms:
(-15 + 5x)(-18 + 6x) = 0

Multiply (-15 + 5x) * (-18 + 6x)
(-15(-18 + 6x) + 5x * (-18 + 6x)) = 0
((-18 * -15 + 6x * -15) + 5x * (-18 + 6x)) = 0
((270 + -90x) + 5x * (-18 + 6x)) = 0
(270 + -90x + (-18 * 5x + 6x * 5x)) = 0
(270 + -90x + (-90x + 30x2)) = 0

Combine like terms: -90x + -90x = -180x
(270 + -180x + 30x2) = 0

Solving
270 + -180x + 30x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '30'.
30(9 + -6x + x2) = 0

Factor a trinomial.
30((3 + -1x)(3 + -1x)) = 0

Ignore the factor 30.

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 '(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

Solution

x = {3, 3}

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