x(x+20)=x(2x+3)

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Solution for x(x+20)=x(2x+3) equation: 


Simplifying
x(x + 20) = x(2x + 3)

Reorder the terms:
x(20 + x) = x(2x + 3)
(20 * x + x * x) = x(2x + 3)
(20x + x2) = x(2x + 3)

Reorder the terms:
20x + x2 = x(3 + 2x)
20x + x2 = (3 * x + 2x * x)
20x + x2 = (3x + 2x2)

Solving
20x + x2 = 3x + 2x2

Solving for variable 'x'.

Reorder the terms:
20x + -3x + x2 + -2x2 = 3x + 2x2 + -3x + -2x2

Combine like terms: 20x + -3x = 17x
17x + x2 + -2x2 = 3x + 2x2 + -3x + -2x2

Combine like terms: x2 + -2x2 = -1x2
17x + -1x2 = 3x + 2x2 + -3x + -2x2

Reorder the terms:
17x + -1x2 = 3x + -3x + 2x2 + -2x2

Combine like terms: 3x + -3x = 0
17x + -1x2 = 0 + 2x2 + -2x2
17x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
17x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(17 + -1x) = 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 '(17 + -1x)' equal to zero and attempt to solve:

Simplifying
17 + -1x = 0

Solving
17 + -1x = 0

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

Add '-17' to each side of the equation.
17 + -17 + -1x = 0 + -17

Combine like terms: 17 + -17 = 0
0 + -1x = 0 + -17
-1x = 0 + -17

Combine like terms: 0 + -17 = -17
-1x = -17

Divide each side by '-1'.
x = 17

Simplifying
x = 17
Solution
x = {0, 17}

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