2x=(3x+5)(x+3y)

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


Simplifying
2x = (3x + 5)(x + 3y)

Reorder the terms:
2x = (5 + 3x)(x + 3y)

Multiply (5 + 3x) * (x + 3y)
2x = (5(x + 3y) + 3x * (x + 3y))
2x = ((x * 5 + 3y * 5) + 3x * (x + 3y))
2x = ((5x + 15y) + 3x * (x + 3y))
2x = (5x + 15y + (x * 3x + 3y * 3x))

Reorder the terms:
2x = (5x + 15y + (9xy + 3x2))
2x = (5x + 15y + (9xy + 3x2))

Reorder the terms:
2x = (5x + 9xy + 3x2 + 15y)
2x = (5x + 9xy + 3x2 + 15y)

Solving
2x = 5x + 9xy + 3x2 + 15y

Solving for variable 'x'.

Combine like terms: 2x + -5x = -3x
-3x + -9xy + -3x2 + -15y = 5x + 9xy + 3x2 + 15y + -5x + -9xy + -3x2 + -15y

Reorder the terms:
-3x + -9xy + -3x2 + -15y = 5x + -5x + 9xy + -9xy + 3x2 + -3x2 + 15y + -15y

Combine like terms: 5x + -5x = 0
-3x + -9xy + -3x2 + -15y = 0 + 9xy + -9xy + 3x2 + -3x2 + 15y + -15y
-3x + -9xy + -3x2 + -15y = 9xy + -9xy + 3x2 + -3x2 + 15y + -15y

Combine like terms: 9xy + -9xy = 0
-3x + -9xy + -3x2 + -15y = 0 + 3x2 + -3x2 + 15y + -15y
-3x + -9xy + -3x2 + -15y = 3x2 + -3x2 + 15y + -15y

Combine like terms: 3x2 + -3x2 = 0
-3x + -9xy + -3x2 + -15y = 0 + 15y + -15y
-3x + -9xy + -3x2 + -15y = 15y + -15y

Combine like terms: 15y + -15y = 0
-3x + -9xy + -3x2 + -15y = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(x + 3xy + x2 + 5y) = 0

Ignore the factor -3.

Subproblem 1

Set the factor '(x + 3xy + x2 + 5y)' equal to zero and attempt to solve: Simplifying x + 3xy + x2 + 5y = 0 Solving x + 3xy + x2 + 5y = 0 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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