(a-15)(2a+3)=0

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Solution for (a-15)(2a+3)=0 equation:


Simplifying
(a + -15)(2a + 3) = 0

Reorder the terms:
(-15 + a)(2a + 3) = 0

Reorder the terms:
(-15 + a)(3 + 2a) = 0

Multiply (-15 + a) * (3 + 2a)
(-15(3 + 2a) + a(3 + 2a)) = 0
((3 * -15 + 2a * -15) + a(3 + 2a)) = 0
((-45 + -30a) + a(3 + 2a)) = 0
(-45 + -30a + (3 * a + 2a * a)) = 0
(-45 + -30a + (3a + 2a2)) = 0

Combine like terms: -30a + 3a = -27a
(-45 + -27a + 2a2) = 0

Solving
-45 + -27a + 2a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -2a)(15 + -1a) = 0

Subproblem 1

Set the factor '(-3 + -2a)' equal to zero and attempt to solve: Simplifying -3 + -2a = 0 Solving -3 + -2a = 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 + -2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2a = 0 + 3 -2a = 0 + 3 Combine like terms: 0 + 3 = 3 -2a = 3 Divide each side by '-2'. a = -1.5 Simplifying a = -1.5

Subproblem 2

Set the factor '(15 + -1a)' equal to zero and attempt to solve: Simplifying 15 + -1a = 0 Solving 15 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + -1a = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -1a = 0 + -15 -1a = 0 + -15 Combine like terms: 0 + -15 = -15 -1a = -15 Divide each side by '-1'. a = 15 Simplifying a = 15

Solution

a = {-1.5, 15}

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