-6(5a+8)(6a-5)=0

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Solution for -6(5a+8)(6a-5)=0 equation: 


Simplifying
-6(5a + 8)(6a + -5) = 0

Reorder the terms:
-6(8 + 5a)(6a + -5) = 0

Reorder the terms:
-6(8 + 5a)(-5 + 6a) = 0

Multiply (8 + 5a) * (-5 + 6a)
-6(8(-5 + 6a) + 5a * (-5 + 6a)) = 0
-6((-5 * 8 + 6a * 8) + 5a * (-5 + 6a)) = 0
-6((-40 + 48a) + 5a * (-5 + 6a)) = 0
-6(-40 + 48a + (-5 * 5a + 6a * 5a)) = 0
-6(-40 + 48a + (-25a + 30a2)) = 0

Combine like terms: 48a + -25a = 23a
-6(-40 + 23a + 30a2) = 0
(-40 * -6 + 23a * -6 + 30a2 * -6) = 0
(240 + -138a + -180a2) = 0

Solving
240 + -138a + -180a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(40 + -23a + -30a2) = 0

Factor a trinomial.
6((5 + -6a)(8 + 5a)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(5 + -6a)' equal to zero and attempt to solve:

Simplifying
5 + -6a = 0

Solving
5 + -6a = 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 + -6a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6a = 0 + -5
-6a = 0 + -5

Combine like terms: 0 + -5 = -5
-6a = -5

Divide each side by '-6'.
a = 0.8333333333

Simplifying
a = 0.8333333333

Subproblem 2
Set the factor '(8 + 5a)' equal to zero and attempt to solve:

Simplifying
8 + 5a = 0

Solving
8 + 5a = 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 + 5a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5a = 0 + -8
5a = 0 + -8

Combine like terms: 0 + -8 = -8
5a = -8

Divide each side by '5'.
a = -1.6

Simplifying
a = -1.6
Solution
a = {0.8333333333, -1.6}

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