(3x-6)(9x-10)=0

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Solution for (3x-6)(9x-10)=0 equation:


Simplifying
(3x + -6)(9x + -10) = 0

Reorder the terms:
(-6 + 3x)(9x + -10) = 0

Reorder the terms:
(-6 + 3x)(-10 + 9x) = 0

Multiply (-6 + 3x) * (-10 + 9x)
(-6(-10 + 9x) + 3x * (-10 + 9x)) = 0
((-10 * -6 + 9x * -6) + 3x * (-10 + 9x)) = 0
((60 + -54x) + 3x * (-10 + 9x)) = 0
(60 + -54x + (-10 * 3x + 9x * 3x)) = 0
(60 + -54x + (-30x + 27x2)) = 0

Combine like terms: -54x + -30x = -84x
(60 + -84x + 27x2) = 0

Solving
60 + -84x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + -28x + 9x2) = 0

Factor a trinomial.
3((10 + -9x)(2 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(10 + -9x)' equal to zero and attempt to solve: Simplifying 10 + -9x = 0 Solving 10 + -9x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -9x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -9x = 0 + -10 -9x = 0 + -10 Combine like terms: 0 + -10 = -10 -9x = -10 Divide each side by '-9'. x = 1.111111111 Simplifying x = 1.111111111

Subproblem 2

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

Solution

x = {1.111111111, 2}

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