2x(x+3)=5x(x-1)

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Solution for 2x(x+3)=5x(x-1) equation: 


Simplifying
2x(x + 3) = 5x(x + -1)

Reorder the terms:
2x(3 + x) = 5x(x + -1)
(3 * 2x + x * 2x) = 5x(x + -1)
(6x + 2x2) = 5x(x + -1)

Reorder the terms:
6x + 2x2 = 5x(-1 + x)
6x + 2x2 = (-1 * 5x + x * 5x)
6x + 2x2 = (-5x + 5x2)

Solving
6x + 2x2 = -5x + 5x2

Solving for variable 'x'.

Reorder the terms:
6x + 5x + 2x2 + -5x2 = -5x + 5x2 + 5x + -5x2

Combine like terms: 6x + 5x = 11x
11x + 2x2 + -5x2 = -5x + 5x2 + 5x + -5x2

Combine like terms: 2x2 + -5x2 = -3x2
11x + -3x2 = -5x + 5x2 + 5x + -5x2

Reorder the terms:
11x + -3x2 = -5x + 5x + 5x2 + -5x2

Combine like terms: -5x + 5x = 0
11x + -3x2 = 0 + 5x2 + -5x2
11x + -3x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
11x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(11 + -3x) = 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 '(11 + -3x)' equal to zero and attempt to solve:

Simplifying
11 + -3x = 0

Solving
11 + -3x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3x = 0 + -11
-3x = 0 + -11

Combine like terms: 0 + -11 = -11
-3x = -11

Divide each side by '-3'.
x = 3.666666667

Simplifying
x = 3.666666667
Solution
x = {0, 3.666666667}

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