(13a+7)(6a-7)=0

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Solution for (13a+7)(6a-7)=0 equation: 


Simplifying
(13a + 7)(6a + -7) = 0

Reorder the terms:
(7 + 13a)(6a + -7) = 0

Reorder the terms:
(7 + 13a)(-7 + 6a) = 0

Multiply (7 + 13a) * (-7 + 6a)
(7(-7 + 6a) + 13a * (-7 + 6a)) = 0
((-7 * 7 + 6a * 7) + 13a * (-7 + 6a)) = 0
((-49 + 42a) + 13a * (-7 + 6a)) = 0
(-49 + 42a + (-7 * 13a + 6a * 13a)) = 0
(-49 + 42a + (-91a + 78a2)) = 0

Combine like terms: 42a + -91a = -49a
(-49 + -49a + 78a2) = 0

Solving
-49 + -49a + 78a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-7 + -13a)(7 + -6a) = 0


Subproblem 1
Set the factor '(-7 + -13a)' equal to zero and attempt to solve:

Simplifying
-7 + -13a = 0

Solving
-7 + -13a = 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 + -13a = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -13a = 0 + 7
-13a = 0 + 7

Combine like terms: 0 + 7 = 7
-13a = 7

Divide each side by '-13'.
a = -0.5384615385

Simplifying
a = -0.5384615385

Subproblem 2
Set the factor '(7 + -6a)' equal to zero and attempt to solve:

Simplifying
7 + -6a = 0

Solving
7 + -6a = 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 + -6a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -6a = 0 + -7
-6a = 0 + -7

Combine like terms: 0 + -7 = -7
-6a = -7

Divide each side by '-6'.
a = 1.166666667

Simplifying
a = 1.166666667
Solution
a = {-0.5384615385, 1.166666667}

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