a(a-13)(2a+9)=0

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Solution for a(a-13)(2a+9)=0 equation: 


Simplifying
a(a + -13)(2a + 9) = 0

Reorder the terms:
a(-13 + a)(2a + 9) = 0

Reorder the terms:
a(-13 + a)(9 + 2a) = 0

Multiply (-13 + a) * (9 + 2a)
a(-13(9 + 2a) + a(9 + 2a)) = 0
a((9 * -13 + 2a * -13) + a(9 + 2a)) = 0
a((-117 + -26a) + a(9 + 2a)) = 0
a(-117 + -26a + (9 * a + 2a * a)) = 0
a(-117 + -26a + (9a + 2a2)) = 0

Combine like terms: -26a + 9a = -17a
a(-117 + -17a + 2a2) = 0
(-117 * a + -17a * a + 2a2 * a) = 0
(-117a + -17a2 + 2a3) = 0

Solving
-117a + -17a2 + 2a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-117 + -17a + 2a2) = 0

Factor a trinomial.
a((-9 + -2a)(13 + -1a)) = 0


Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(-9 + -2a)' equal to zero and attempt to solve:

Simplifying
-9 + -2a = 0

Solving
-9 + -2a = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2a = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2a = 0 + 9
-2a = 0 + 9

Combine like terms: 0 + 9 = 9
-2a = 9

Divide each side by '-2'.
a = -4.5

Simplifying
a = -4.5

Subproblem 3
Set the factor '(13 + -1a)' equal to zero and attempt to solve:

Simplifying
13 + -1a = 0

Solving
13 + -1a = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1a = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1a = 0 + -13
-1a = 0 + -13

Combine like terms: 0 + -13 = -13
-1a = -13

Divide each side by '-1'.
a = 13

Simplifying
a = 13
Solution
a = {0, -4.5, 13}

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