(2a-14)(14a-2)=0

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Solution for (2a-14)(14a-2)=0 equation: 


Simplifying
(2a + -14)(14a + -2) = 0

Reorder the terms:
(-14 + 2a)(14a + -2) = 0

Reorder the terms:
(-14 + 2a)(-2 + 14a) = 0

Multiply (-14 + 2a) * (-2 + 14a)
(-14(-2 + 14a) + 2a * (-2 + 14a)) = 0
((-2 * -14 + 14a * -14) + 2a * (-2 + 14a)) = 0
((28 + -196a) + 2a * (-2 + 14a)) = 0
(28 + -196a + (-2 * 2a + 14a * 2a)) = 0
(28 + -196a + (-4a + 28a2)) = 0

Combine like terms: -196a + -4a = -200a
(28 + -200a + 28a2) = 0

Solving
28 + -200a + 28a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -50a + 7a2) = 0

Factor a trinomial.
4((1 + -7a)(7 + -1a)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + -7a)' equal to zero and attempt to solve:

Simplifying
1 + -7a = 0

Solving
1 + -7a = 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 + -7a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7a = 0 + -1
-7a = 0 + -1

Combine like terms: 0 + -1 = -1
-7a = -1

Divide each side by '-7'.
a = 0.1428571429

Simplifying
a = 0.1428571429

Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {0.1428571429, 7}

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