x(x+5)=x(3x)

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Solution for x(x+5)=x(3x) equation: 


Simplifying
x(x + 5) = x(3x)

Reorder the terms:
x(5 + x) = x(3x)
(5 * x + x * x) = x(3x)
(5x + x2) = x(3x)

Remove parenthesis around (3x)
5x + x2 = x * 3x

Reorder the terms for easier multiplication:
5x + x2 = 3x * x

Multiply x * x
5x + x2 = 3x2

Solving
5x + x2 = 3x2

Solving for variable 'x'.

Combine like terms: x2 + -3x2 = -2x2
5x + -2x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
5x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + -2x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0, 2.5}

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