5a(7a-5)(5a-1)=0

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Solution for 5a(7a-5)(5a-1)=0 equation: 


Simplifying
5a(7a + -5)(5a + -1) = 0

Reorder the terms:
5a(-5 + 7a)(5a + -1) = 0

Reorder the terms:
5a(-5 + 7a)(-1 + 5a) = 0

Multiply (-5 + 7a) * (-1 + 5a)
5a(-5(-1 + 5a) + 7a * (-1 + 5a)) = 0
5a((-1 * -5 + 5a * -5) + 7a * (-1 + 5a)) = 0
5a((5 + -25a) + 7a * (-1 + 5a)) = 0
5a(5 + -25a + (-1 * 7a + 5a * 7a)) = 0
5a(5 + -25a + (-7a + 35a2)) = 0

Combine like terms: -25a + -7a = -32a
5a(5 + -32a + 35a2) = 0
(5 * 5a + -32a * 5a + 35a2 * 5a) = 0
(25a + -160a2 + 175a3) = 0

Solving
25a + -160a2 + 175a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '5a'.
5a(5 + -32a + 35a2) = 0

Factor a trinomial.
5a((1 + -5a)(5 + -7a)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(1 + -5a)' equal to zero and attempt to solve:

Simplifying
1 + -5a = 0

Solving
1 + -5a = 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 + -5a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5a = 0 + -1
-5a = 0 + -1

Combine like terms: 0 + -1 = -1
-5a = -1

Divide each side by '-5'.
a = 0.2

Simplifying
a = 0.2

Subproblem 3
Set the factor '(5 + -7a)' equal to zero and attempt to solve:

Simplifying
5 + -7a = 0

Solving
5 + -7a = 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 + -7a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7a = 0 + -5
-7a = 0 + -5

Combine like terms: 0 + -5 = -5
-7a = -5

Divide each side by '-7'.
a = 0.7142857143

Simplifying
a = 0.7142857143
Solution
a = {0, 0.2, 0.7142857143}

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