(a-2)(a-4)=0

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Solution for (a-2)(a-4)=0 equation:


Simplifying
(a + -2)(a + -4) = 0

Reorder the terms:
(-2 + a)(a + -4) = 0

Reorder the terms:
(-2 + a)(-4 + a) = 0

Multiply (-2 + a) * (-4 + a)
(-2(-4 + a) + a(-4 + a)) = 0
((-4 * -2 + a * -2) + a(-4 + a)) = 0
((8 + -2a) + a(-4 + a)) = 0
(8 + -2a + (-4 * a + a * a)) = 0
(8 + -2a + (-4a + a2)) = 0

Combine like terms: -2a + -4a = -6a
(8 + -6a + a2) = 0

Solving
8 + -6a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2 + -1a)(4 + -1a) = 0

Subproblem 1

Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2

Subproblem 2

Set the factor '(4 + -1a)' equal to zero and attempt to solve: Simplifying 4 + -1a = 0 Solving 4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1a = 0 + -4 -1a = 0 + -4 Combine like terms: 0 + -4 = -4 -1a = -4 Divide each side by '-1'. a = 4 Simplifying a = 4

Solution

a = {2, 4}

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