-2(a-5)(a-7)=0

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Solution for -2(a-5)(a-7)=0 equation: 


Simplifying
-2(a + -5)(a + -7) = 0

Reorder the terms:
-2(-5 + a)(a + -7) = 0

Reorder the terms:
-2(-5 + a)(-7 + a) = 0

Multiply (-5 + a) * (-7 + a)
-2(-5(-7 + a) + a(-7 + a)) = 0
-2((-7 * -5 + a * -5) + a(-7 + a)) = 0
-2((35 + -5a) + a(-7 + a)) = 0
-2(35 + -5a + (-7 * a + a * a)) = 0
-2(35 + -5a + (-7a + a2)) = 0

Combine like terms: -5a + -7a = -12a
-2(35 + -12a + a2) = 0
(35 * -2 + -12a * -2 + a2 * -2) = 0
(-70 + 24a + -2a2) = 0

Solving
-70 + 24a + -2a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-35 + 12a + -1a2) = 0

Factor a trinomial.
2((-7 + a)(5 + -1a)) = 0

Ignore the factor 2.

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

Simplifying
-7 + a = 0

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

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

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

Simplifying
a = 7

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

Simplifying
5 + -1a = 0

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

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

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

Divide each side by '-1'.
a = 5

Simplifying
a = 5
Solution
a = {7, 5}

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