(8a+5)(3a-4)=0

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Solution for (8a+5)(3a-4)=0 equation:


Simplifying
(8a + 5)(3a + -4) = 0

Reorder the terms:
(5 + 8a)(3a + -4) = 0

Reorder the terms:
(5 + 8a)(-4 + 3a) = 0

Multiply (5 + 8a) * (-4 + 3a)
(5(-4 + 3a) + 8a * (-4 + 3a)) = 0
((-4 * 5 + 3a * 5) + 8a * (-4 + 3a)) = 0
((-20 + 15a) + 8a * (-4 + 3a)) = 0
(-20 + 15a + (-4 * 8a + 3a * 8a)) = 0
(-20 + 15a + (-32a + 24a2)) = 0

Combine like terms: 15a + -32a = -17a
(-20 + -17a + 24a2) = 0

Solving
-20 + -17a + 24a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -8a)(4 + -3a) = 0

Subproblem 1

Set the factor '(-5 + -8a)' equal to zero and attempt to solve: Simplifying -5 + -8a = 0 Solving -5 + -8a = 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 + -8a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -8a = 0 + 5 -8a = 0 + 5 Combine like terms: 0 + 5 = 5 -8a = 5 Divide each side by '-8'. a = -0.625 Simplifying a = -0.625

Subproblem 2

Set the factor '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333

Solution

a = {-0.625, 1.333333333}

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