(3a-9)(a-9)=0

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Solution for (3a-9)(a-9)=0 equation:


Simplifying
(3a + -9)(a + -9) = 0

Reorder the terms:
(-9 + 3a)(a + -9) = 0

Reorder the terms:
(-9 + 3a)(-9 + a) = 0

Multiply (-9 + 3a) * (-9 + a)
(-9(-9 + a) + 3a * (-9 + a)) = 0
((-9 * -9 + a * -9) + 3a * (-9 + a)) = 0
((81 + -9a) + 3a * (-9 + a)) = 0
(81 + -9a + (-9 * 3a + a * 3a)) = 0
(81 + -9a + (-27a + 3a2)) = 0

Combine like terms: -9a + -27a = -36a
(81 + -36a + 3a2) = 0

Solving
81 + -36a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(27 + -12a + a2) = 0

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

Ignore the factor 3.

Subproblem 1

Set the factor '(3 + -1a)' equal to zero and attempt to solve: Simplifying 3 + -1a = 0 Solving 3 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1a = 0 + -3 -1a = 0 + -3 Combine like terms: 0 + -3 = -3 -1a = -3 Divide each side by '-1'. a = 3 Simplifying a = 3

Subproblem 2

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

Solution

a = {3, 9}

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