=2x(3x+5y)

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


Simplifying
0 = 2x(3x + 5y)
0 = (3x * 2x + 5y * 2x)

Reorder the terms:
0 = (10xy + 6x2)
0 = (10xy + 6x2)

Solving
0 = 10xy + 6x2

Solving for variable 'x'.
Remove the zero:
-10xy + -6x2 = 10xy + 6x2 + -10xy + -6x2

Reorder the terms:
-10xy + -6x2 = 10xy + -10xy + 6x2 + -6x2

Combine like terms: 10xy + -10xy = 0
-10xy + -6x2 = 0 + 6x2 + -6x2
-10xy + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-10xy + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-2x'.
-2x(5y + 3x) = 0

Ignore the factor -2.

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 '(5y + 3x)' equal to zero and attempt to solve: Simplifying 5y + 3x = 0 Reorder the terms: 3x + 5y = 0 Solving 3x + 5y = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y' to each side of the equation. 3x + 5y + -5y = 0 + -5y Combine like terms: 5y + -5y = 0 3x + 0 = 0 + -5y 3x = 0 + -5y Remove the zero: 3x = -5y Divide each side by '3'. x = -1.666666667y Simplifying x = -1.666666667y

Solution

x = {0, -1.666666667y}

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