5a(a+3)=2a(2a-5)

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Solution for 5a(a+3)=2a(2a-5) equation: 


Simplifying
5a(a + 3) = 2a(2a + -5)

Reorder the terms:
5a(3 + a) = 2a(2a + -5)
(3 * 5a + a * 5a) = 2a(2a + -5)
(15a + 5a2) = 2a(2a + -5)

Reorder the terms:
15a + 5a2 = 2a(-5 + 2a)
15a + 5a2 = (-5 * 2a + 2a * 2a)
15a + 5a2 = (-10a + 4a2)

Solving
15a + 5a2 = -10a + 4a2

Solving for variable 'a'.

Reorder the terms:
15a + 10a + 5a2 + -4a2 = -10a + 4a2 + 10a + -4a2

Combine like terms: 15a + 10a = 25a
25a + 5a2 + -4a2 = -10a + 4a2 + 10a + -4a2

Combine like terms: 5a2 + -4a2 = 1a2
25a + 1a2 = -10a + 4a2 + 10a + -4a2

Reorder the terms:
25a + 1a2 = -10a + 10a + 4a2 + -4a2

Combine like terms: -10a + 10a = 0
25a + 1a2 = 0 + 4a2 + -4a2
25a + 1a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
25a + 1a2 = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(25 + a) = 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 '(25 + a)' equal to zero and attempt to solve:

Simplifying
25 + a = 0

Solving
25 + a = 0

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

Add '-25' to each side of the equation.
25 + -25 + a = 0 + -25

Combine like terms: 25 + -25 = 0
0 + a = 0 + -25
a = 0 + -25

Combine like terms: 0 + -25 = -25
a = -25

Simplifying
a = -25
Solution
a = {0, -25}

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