3(a-5)(a+2)=0

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Solution for 3(a-5)(a+2)=0 equation:


Simplifying
3(a + -5)(a + 2) = 0

Reorder the terms:
3(-5 + a)(a + 2) = 0

Reorder the terms:
3(-5 + a)(2 + a) = 0

Multiply (-5 + a) * (2 + a)
3(-5(2 + a) + a(2 + a)) = 0
3((2 * -5 + a * -5) + a(2 + a)) = 0
3((-10 + -5a) + a(2 + a)) = 0
3(-10 + -5a + (2 * a + a * a)) = 0
3(-10 + -5a + (2a + a2)) = 0

Combine like terms: -5a + 2a = -3a
3(-10 + -3a + a2) = 0
(-10 * 3 + -3a * 3 + a2 * 3) = 0
(-30 + -9a + 3a2) = 0

Solving
-30 + -9a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + -3a + a2) = 0

Factor a trinomial.
3((-2 + -1a)(5 + -1a)) = 0

Ignore the factor 3.

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 '(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 = {-2, 5}

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