6a(2a+4)=5a(5a-6)

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Solution for 6a(2a+4)=5a(5a-6) equation: 


Simplifying
6a(2a + 4) = 5a(5a + -6)

Reorder the terms:
6a(4 + 2a) = 5a(5a + -6)
(4 * 6a + 2a * 6a) = 5a(5a + -6)
(24a + 12a2) = 5a(5a + -6)

Reorder the terms:
24a + 12a2 = 5a(-6 + 5a)
24a + 12a2 = (-6 * 5a + 5a * 5a)
24a + 12a2 = (-30a + 25a2)

Solving
24a + 12a2 = -30a + 25a2

Solving for variable 'a'.

Reorder the terms:
24a + 30a + 12a2 + -25a2 = -30a + 25a2 + 30a + -25a2

Combine like terms: 24a + 30a = 54a
54a + 12a2 + -25a2 = -30a + 25a2 + 30a + -25a2

Combine like terms: 12a2 + -25a2 = -13a2
54a + -13a2 = -30a + 25a2 + 30a + -25a2

Reorder the terms:
54a + -13a2 = -30a + 30a + 25a2 + -25a2

Combine like terms: -30a + 30a = 0
54a + -13a2 = 0 + 25a2 + -25a2
54a + -13a2 = 25a2 + -25a2

Combine like terms: 25a2 + -25a2 = 0
54a + -13a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(54 + -13a) = 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 '(54 + -13a)' equal to zero and attempt to solve:

Simplifying
54 + -13a = 0

Solving
54 + -13a = 0

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

Add '-54' to each side of the equation.
54 + -54 + -13a = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -13a = 0 + -54
-13a = 0 + -54

Combine like terms: 0 + -54 = -54
-13a = -54

Divide each side by '-13'.
a = 4.153846154

Simplifying
a = 4.153846154
Solution
a = {0, 4.153846154}

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