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

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


Simplifying
5a(5a + x) = 2a(2a + -1x)
(5a * 5a + x * 5a) = 2a(2a + -1x)

Reorder the terms:
(5ax + 25a2) = 2a(2a + -1x)
(5ax + 25a2) = 2a(2a + -1x)
5ax + 25a2 = (2a * 2a + -1x * 2a)

Reorder the terms:
5ax + 25a2 = (-2ax + 4a2)
5ax + 25a2 = (-2ax + 4a2)

Solving
5ax + 25a2 = -2ax + 4a2

Solving for variable 'a'.

Reorder the terms:
5ax + 2ax + 25a2 + -4a2 = -2ax + 4a2 + 2ax + -4a2

Combine like terms: 5ax + 2ax = 7ax
7ax + 25a2 + -4a2 = -2ax + 4a2 + 2ax + -4a2

Combine like terms: 25a2 + -4a2 = 21a2
7ax + 21a2 = -2ax + 4a2 + 2ax + -4a2

Reorder the terms:
7ax + 21a2 = -2ax + 2ax + 4a2 + -4a2

Combine like terms: -2ax + 2ax = 0
7ax + 21a2 = 0 + 4a2 + -4a2
7ax + 21a2 = 4a2 + -4a2

Combine like terms: 4a2 + -4a2 = 0
7ax + 21a2 = 0

Factor out the Greatest Common Factor (GCF), '7a'.
7a(x + 3a) = 0

Ignore the factor 7.

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

Simplifying
x + 3a = 0

Reorder the terms:
3a + x = 0

Solving
3a + x = 0

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

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

Combine like terms: x + -1x = 0
3a + 0 = 0 + -1x
3a = 0 + -1x
Remove the zero:
3a = -1x

Divide each side by '3'.
a = -0.3333333333x

Simplifying
a = -0.3333333333x
Solution
a = {0, -0.3333333333x}

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