(5a-8)(4a-2)=0

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Solution for (5a-8)(4a-2)=0 equation: 


Simplifying
(5a + -8)(4a + -2) = 0

Reorder the terms:
(-8 + 5a)(4a + -2) = 0

Reorder the terms:
(-8 + 5a)(-2 + 4a) = 0

Multiply (-8 + 5a) * (-2 + 4a)
(-8(-2 + 4a) + 5a * (-2 + 4a)) = 0
((-2 * -8 + 4a * -8) + 5a * (-2 + 4a)) = 0
((16 + -32a) + 5a * (-2 + 4a)) = 0
(16 + -32a + (-2 * 5a + 4a * 5a)) = 0
(16 + -32a + (-10a + 20a2)) = 0

Combine like terms: -32a + -10a = -42a
(16 + -42a + 20a2) = 0

Solving
16 + -42a + 20a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + -21a + 10a2) = 0

Factor a trinomial.
2((1 + -2a)(8 + -5a)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(1 + -2a)' equal to zero and attempt to solve:

Simplifying
1 + -2a = 0

Solving
1 + -2a = 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 + -2a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2a = 0 + -1
-2a = 0 + -1

Combine like terms: 0 + -1 = -1
-2a = -1

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5

Subproblem 2
Set the factor '(8 + -5a)' equal to zero and attempt to solve:

Simplifying
8 + -5a = 0

Solving
8 + -5a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-8' to each side of the equation.
8 + -8 + -5a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5a = 0 + -8
-5a = 0 + -8

Combine like terms: 0 + -8 = -8
-5a = -8

Divide each side by '-5'.
a = 1.6

Simplifying
a = 1.6
Solution
a = {0.5, 1.6}

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