(5a-4)(3a+2)=0

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Solution for (5a-4)(3a+2)=0 equation:


Simplifying
(5a + -4)(3a + 2) = 0

Reorder the terms:
(-4 + 5a)(3a + 2) = 0

Reorder the terms:
(-4 + 5a)(2 + 3a) = 0

Multiply (-4 + 5a) * (2 + 3a)
(-4(2 + 3a) + 5a * (2 + 3a)) = 0
((2 * -4 + 3a * -4) + 5a * (2 + 3a)) = 0
((-8 + -12a) + 5a * (2 + 3a)) = 0
(-8 + -12a + (2 * 5a + 3a * 5a)) = 0
(-8 + -12a + (10a + 15a2)) = 0

Combine like terms: -12a + 10a = -2a
(-8 + -2a + 15a2) = 0

Solving
-8 + -2a + 15a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -3a)(4 + -5a) = 0

Subproblem 1

Set the factor '(-2 + -3a)' equal to zero and attempt to solve: Simplifying -2 + -3a = 0 Solving -2 + -3a = 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 + -3a = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -3a = 0 + 2 -3a = 0 + 2 Combine like terms: 0 + 2 = 2 -3a = 2 Divide each side by '-3'. a = -0.6666666667 Simplifying a = -0.6666666667

Subproblem 2

Set the factor '(4 + -5a)' equal to zero and attempt to solve: Simplifying 4 + -5a = 0 Solving 4 + -5a = 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 + -5a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5a = 0 + -4 -5a = 0 + -4 Combine like terms: 0 + -4 = -4 -5a = -4 Divide each side by '-5'. a = 0.8 Simplifying a = 0.8

Solution

a = {-0.6666666667, 0.8}

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