(a+5)(a-12)=0

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Solution for (a+5)(a-12)=0 equation:


Simplifying
(a + 5)(a + -12) = 0

Reorder the terms:
(5 + a)(a + -12) = 0

Reorder the terms:
(5 + a)(-12 + a) = 0

Multiply (5 + a) * (-12 + a)
(5(-12 + a) + a(-12 + a)) = 0
((-12 * 5 + a * 5) + a(-12 + a)) = 0
((-60 + 5a) + a(-12 + a)) = 0
(-60 + 5a + (-12 * a + a * a)) = 0
(-60 + 5a + (-12a + a2)) = 0

Combine like terms: 5a + -12a = -7a
(-60 + -7a + a2) = 0

Solving
-60 + -7a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -1a)(12 + -1a) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(12 + -1a)' equal to zero and attempt to solve: Simplifying 12 + -1a = 0 Solving 12 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1a = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1a = 0 + -12 -1a = 0 + -12 Combine like terms: 0 + -12 = -12 -1a = -12 Divide each side by '-1'. a = 12 Simplifying a = 12

Solution

a = {-5, 12}

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