(13a+7)(6a-18)=0

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Solution for (13a+7)(6a-18)=0 equation: 


Simplifying
(13a + 7)(6a + -18) = 0

Reorder the terms:
(7 + 13a)(6a + -18) = 0

Reorder the terms:
(7 + 13a)(-18 + 6a) = 0

Multiply (7 + 13a) * (-18 + 6a)
(7(-18 + 6a) + 13a * (-18 + 6a)) = 0
((-18 * 7 + 6a * 7) + 13a * (-18 + 6a)) = 0
((-126 + 42a) + 13a * (-18 + 6a)) = 0
(-126 + 42a + (-18 * 13a + 6a * 13a)) = 0
(-126 + 42a + (-234a + 78a2)) = 0

Combine like terms: 42a + -234a = -192a
(-126 + -192a + 78a2) = 0

Solving
-126 + -192a + 78a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + -32a + 13a2) = 0

Factor a trinomial.
6((-7 + -13a)(3 + -1a)) = 0

Ignore the factor 6.

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 '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {-0.5384615385, 3}

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