(2a-9)(2a-9)-(a+9)(a+9)=0

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Solution for (2a-9)(2a-9)-(a+9)(a+9)=0 equation:


Simplifying
(2a + -9)(2a + -9) + -1(a + 9)(a + 9) = 0

Reorder the terms:
(-9 + 2a)(2a + -9) + -1(a + 9)(a + 9) = 0

Reorder the terms:
(-9 + 2a)(-9 + 2a) + -1(a + 9)(a + 9) = 0

Multiply (-9 + 2a) * (-9 + 2a)
(-9(-9 + 2a) + 2a * (-9 + 2a)) + -1(a + 9)(a + 9) = 0
((-9 * -9 + 2a * -9) + 2a * (-9 + 2a)) + -1(a + 9)(a + 9) = 0
((81 + -18a) + 2a * (-9 + 2a)) + -1(a + 9)(a + 9) = 0
(81 + -18a + (-9 * 2a + 2a * 2a)) + -1(a + 9)(a + 9) = 0
(81 + -18a + (-18a + 4a2)) + -1(a + 9)(a + 9) = 0

Combine like terms: -18a + -18a = -36a
(81 + -36a + 4a2) + -1(a + 9)(a + 9) = 0

Reorder the terms:
81 + -36a + 4a2 + -1(9 + a)(a + 9) = 0

Reorder the terms:
81 + -36a + 4a2 + -1(9 + a)(9 + a) = 0

Multiply (9 + a) * (9 + a)
81 + -36a + 4a2 + -1(9(9 + a) + a(9 + a)) = 0
81 + -36a + 4a2 + -1((9 * 9 + a * 9) + a(9 + a)) = 0
81 + -36a + 4a2 + -1((81 + 9a) + a(9 + a)) = 0
81 + -36a + 4a2 + -1(81 + 9a + (9 * a + a * a)) = 0
81 + -36a + 4a2 + -1(81 + 9a + (9a + a2)) = 0

Combine like terms: 9a + 9a = 18a
81 + -36a + 4a2 + -1(81 + 18a + a2) = 0
81 + -36a + 4a2 + (81 * -1 + 18a * -1 + a2 * -1) = 0
81 + -36a + 4a2 + (-81 + -18a + -1a2) = 0

Reorder the terms:
81 + -81 + -36a + -18a + 4a2 + -1a2 = 0

Combine like terms: 81 + -81 = 0
0 + -36a + -18a + 4a2 + -1a2 = 0
-36a + -18a + 4a2 + -1a2 = 0

Combine like terms: -36a + -18a = -54a
-54a + 4a2 + -1a2 = 0

Combine like terms: 4a2 + -1a2 = 3a2
-54a + 3a2 = 0

Solving
-54a + 3a2 = 0

Solving for variable 'a'.

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

Ignore the factor 3.

Subproblem 1

Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0

Subproblem 2

Set the factor '(-18 + a)' equal to zero and attempt to solve: Simplifying -18 + a = 0 Solving -18 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '18' to each side of the equation. -18 + 18 + a = 0 + 18 Combine like terms: -18 + 18 = 0 0 + a = 0 + 18 a = 0 + 18 Combine like terms: 0 + 18 = 18 a = 18 Simplifying a = 18

Solution

a = {0, 18}

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