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

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


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

Reorder the terms:
(-1a + 5x)(x + -2a) = 5x(x + -1a)

Reorder the terms:
(-1a + 5x)(-2a + x) = 5x(x + -1a)

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

Reorder the terms:
((-1ax + 2a2) + 5x * (-2a + x)) = 5x(x + -1a)
((-1ax + 2a2) + 5x * (-2a + x)) = 5x(x + -1a)
(-1ax + 2a2 + (-2a * 5x + x * 5x)) = 5x(x + -1a)
(-1ax + 2a2 + (-10ax + 5x2)) = 5x(x + -1a)

Reorder the terms:
(-1ax + -10ax + 2a2 + 5x2) = 5x(x + -1a)

Combine like terms: -1ax + -10ax = -11ax
(-11ax + 2a2 + 5x2) = 5x(x + -1a)

Reorder the terms:
-11ax + 2a2 + 5x2 = 5x(-1a + x)
-11ax + 2a2 + 5x2 = (-1a * 5x + x * 5x)
-11ax + 2a2 + 5x2 = (-5ax + 5x2)

Add '-5x2' to each side of the equation.
-11ax + 2a2 + 5x2 + -5x2 = -5ax + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-11ax + 2a2 + 0 = -5ax + 5x2 + -5x2
-11ax + 2a2 = -5ax + 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-11ax + 2a2 = -5ax + 0
-11ax + 2a2 = -5ax

Solving
-11ax + 2a2 = -5ax

Solving for variable 'a'.

Reorder the terms:
-11ax + 5ax + 2a2 = -5ax + 5ax

Combine like terms: -11ax + 5ax = -6ax
-6ax + 2a2 = -5ax + 5ax

Combine like terms: -5ax + 5ax = 0
-6ax + 2a2 = 0

Factor out the Greatest Common Factor (GCF), '2a'.
2a(-3x + a) = 0

Ignore the factor 2.

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

Simplifying
-3x + a = 0

Reorder the terms:
a + -3x = 0

Solving
a + -3x = 0

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

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

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

Simplifying
a = 3x
Solution
a = {0, 3x}

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