2a(7a-2)(2a-1)=0

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Solution for 2a(7a-2)(2a-1)=0 equation: 


Simplifying
2a(7a + -2)(2a + -1) = 0

Reorder the terms:
2a(-2 + 7a)(2a + -1) = 0

Reorder the terms:
2a(-2 + 7a)(-1 + 2a) = 0

Multiply (-2 + 7a) * (-1 + 2a)
2a(-2(-1 + 2a) + 7a * (-1 + 2a)) = 0
2a((-1 * -2 + 2a * -2) + 7a * (-1 + 2a)) = 0
2a((2 + -4a) + 7a * (-1 + 2a)) = 0
2a(2 + -4a + (-1 * 7a + 2a * 7a)) = 0
2a(2 + -4a + (-7a + 14a2)) = 0

Combine like terms: -4a + -7a = -11a
2a(2 + -11a + 14a2) = 0
(2 * 2a + -11a * 2a + 14a2 * 2a) = 0
(4a + -22a2 + 28a3) = 0

Solving
4a + -22a2 + 28a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2a'.
2a(2 + -11a + 14a2) = 0

Factor a trinomial.
2a((2 + -7a)(1 + -2a)) = 0

Ignore the factor 2.

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 '(2 + -7a)' equal to zero and attempt to solve:

Simplifying
2 + -7a = 0

Solving
2 + -7a = 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 + -7a = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7a = 0 + -2
-7a = 0 + -2

Combine like terms: 0 + -2 = -2
-7a = -2

Divide each side by '-7'.
a = 0.2857142857

Simplifying
a = 0.2857142857

Subproblem 3
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
Solution
a = {0, 0.2857142857, 0.5}

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