(a+6)(a-5)=0

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Solution for (a+6)(a-5)=0 equation:


Simplifying
(a + 6)(a + -5) = 0

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

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

Multiply (6 + a) * (-5 + a)
(6(-5 + a) + a(-5 + a)) = 0
((-5 * 6 + a * 6) + a(-5 + a)) = 0
((-30 + 6a) + a(-5 + a)) = 0
(-30 + 6a + (-5 * a + a * a)) = 0
(-30 + 6a + (-5a + a2)) = 0

Combine like terms: 6a + -5a = 1a
(-30 + 1a + a2) = 0

Solving
-30 + 1a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-6 + -1a)(5 + -1a) = 0

Subproblem 1

Set the factor '(-6 + -1a)' equal to zero and attempt to solve: Simplifying -6 + -1a = 0 Solving -6 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1a = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1a = 0 + 6 -1a = 0 + 6 Combine like terms: 0 + 6 = 6 -1a = 6 Divide each side by '-1'. a = -6 Simplifying a = -6

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 = {-6, 5}

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