a(a-3)+6-2a=0

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Solution for a(a-3)+6-2a=0 equation:


Simplifying
a(a + -3) + 6 + -2a = 0

Reorder the terms:
a(-3 + a) + 6 + -2a = 0
(-3 * a + a * a) + 6 + -2a = 0
(-3a + a2) + 6 + -2a = 0

Reorder the terms:
6 + -3a + -2a + a2 = 0

Combine like terms: -3a + -2a = -5a
6 + -5a + a2 = 0

Solving
6 + -5a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2 + -1a)(3 + -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 '(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

Solution

a = {2, 3}

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