(2a-5)(3a+1)=0

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Solution for (2a-5)(3a+1)=0 equation:


Simplifying
(2a + -5)(3a + 1) = 0

Reorder the terms:
(-5 + 2a)(3a + 1) = 0

Reorder the terms:
(-5 + 2a)(1 + 3a) = 0

Multiply (-5 + 2a) * (1 + 3a)
(-5(1 + 3a) + 2a * (1 + 3a)) = 0
((1 * -5 + 3a * -5) + 2a * (1 + 3a)) = 0
((-5 + -15a) + 2a * (1 + 3a)) = 0
(-5 + -15a + (1 * 2a + 3a * 2a)) = 0
(-5 + -15a + (2a + 6a2)) = 0

Combine like terms: -15a + 2a = -13a
(-5 + -13a + 6a2) = 0

Solving
-5 + -13a + 6a2 = 0

Solving for variable 'a'.

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

Subproblem 1

Set the factor '(-1 + -3a)' equal to zero and attempt to solve: Simplifying -1 + -3a = 0 Solving -1 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -3a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3a = 0 + 1 -3a = 0 + 1 Combine like terms: 0 + 1 = 1 -3a = 1 Divide each side by '-3'. a = -0.3333333333 Simplifying a = -0.3333333333

Subproblem 2

Set the factor '(5 + -2a)' equal to zero and attempt to solve: Simplifying 5 + -2a = 0 Solving 5 + -2a = 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 + -2a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2a = 0 + -5 -2a = 0 + -5 Combine like terms: 0 + -5 = -5 -2a = -5 Divide each side by '-2'. a = 2.5 Simplifying a = 2.5

Solution

a = {-0.3333333333, 2.5}

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