(2a-10)(a+3)=0

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Solution for (2a-10)(a+3)=0 equation:


Simplifying
(2a + -10)(a + 3) = 0

Reorder the terms:
(-10 + 2a)(a + 3) = 0

Reorder the terms:
(-10 + 2a)(3 + a) = 0

Multiply (-10 + 2a) * (3 + a)
(-10(3 + a) + 2a * (3 + a)) = 0
((3 * -10 + a * -10) + 2a * (3 + a)) = 0
((-30 + -10a) + 2a * (3 + a)) = 0
(-30 + -10a + (3 * 2a + a * 2a)) = 0
(-30 + -10a + (6a + 2a2)) = 0

Combine like terms: -10a + 6a = -4a
(-30 + -4a + 2a2) = 0

Solving
-30 + -4a + 2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + -2a + a2) = 0

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

Ignore the factor 2.

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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