(7a-14)(a+8)=0

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Solution for (7a-14)(a+8)=0 equation: 


Simplifying
(7a + -14)(a + 8) = 0

Reorder the terms:
(-14 + 7a)(a + 8) = 0

Reorder the terms:
(-14 + 7a)(8 + a) = 0

Multiply (-14 + 7a) * (8 + a)
(-14(8 + a) + 7a * (8 + a)) = 0
((8 * -14 + a * -14) + 7a * (8 + a)) = 0
((-112 + -14a) + 7a * (8 + a)) = 0
(-112 + -14a + (8 * 7a + a * 7a)) = 0
(-112 + -14a + (56a + 7a2)) = 0

Combine like terms: -14a + 56a = 42a
(-112 + 42a + 7a2) = 0

Solving
-112 + 42a + 7a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-16 + 6a + a2) = 0

Factor a trinomial.
7((-8 + -1a)(2 + -1a)) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-8 + -1a)' equal to zero and attempt to solve:

Simplifying
-8 + -1a = 0

Solving
-8 + -1a = 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 + -1a = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1a = 0 + 8
-1a = 0 + 8

Combine like terms: 0 + 8 = 8
-1a = 8

Divide each side by '-1'.
a = -8

Simplifying
a = -8

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

Simplifying
2 + -1a = 0

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

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

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

Divide each side by '-1'.
a = 2

Simplifying
a = 2
Solution
a = {-8, 2}

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