3x(2x+3)-5x=0

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Solution for 3x(2x+3)-5x=0 equation: 


Simplifying
3x(2x + 3) + -5x = 0

Reorder the terms:
3x(3 + 2x) + -5x = 0
(3 * 3x + 2x * 3x) + -5x = 0
(9x + 6x2) + -5x = 0

Reorder the terms:
9x + -5x + 6x2 = 0

Combine like terms: 9x + -5x = 4x
4x + 6x2 = 0

Solving
4x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(2 + 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 '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 0

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

Add '-2' to each side of the equation.
2 + -2 + 3x = 0 + -2

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

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

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {0, -0.6666666667}

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