(a+3)(a-5)=0

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Solution for (a+3)(a-5)=0 equation:


Simplifying
(a + 3)(a + -5) = 0

Reorder the terms:
(3 + a)(a + -5) = 0

Reorder the terms:
(3 + a)(-5 + a) = 0

Multiply (3 + a) * (-5 + a)
(3(-5 + a) + a(-5 + a)) = 0
((-5 * 3 + a * 3) + a(-5 + a)) = 0
((-15 + 3a) + a(-5 + a)) = 0
(-15 + 3a + (-5 * a + a * a)) = 0
(-15 + 3a + (-5a + a2)) = 0

Combine like terms: 3a + -5a = -2a
(-15 + -2a + a2) = 0

Solving
-15 + -2a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -1a)(5 + -1a) = 0

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 '(5 + -1a)' equal to zero and attempt to solve: Simplifying 5 + -1a = 0 Solving 5 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1a = 0 + -5 -1a = 0 + -5 Combine like terms: 0 + -5 = -5 -1a = -5 Divide each side by '-1'. a = 5 Simplifying a = 5

Solution

a = {-3, 5}

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