(2x+3)(3x-2)+6=0

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Solution for (2x+3)(3x-2)+6=0 equation: 


Simplifying
(2x + 3)(3x + -2) + 6 = 0

Reorder the terms:
(3 + 2x)(3x + -2) + 6 = 0

Reorder the terms:
(3 + 2x)(-2 + 3x) + 6 = 0

Multiply (3 + 2x) * (-2 + 3x)
(3(-2 + 3x) + 2x * (-2 + 3x)) + 6 = 0
((-2 * 3 + 3x * 3) + 2x * (-2 + 3x)) + 6 = 0
((-6 + 9x) + 2x * (-2 + 3x)) + 6 = 0
(-6 + 9x + (-2 * 2x + 3x * 2x)) + 6 = 0
(-6 + 9x + (-4x + 6x2)) + 6 = 0

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

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

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

Solving
5x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + 6x) = 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 '(5 + 6x)' equal to zero and attempt to solve:

Simplifying
5 + 6x = 0

Solving
5 + 6x = 0

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

Add '-5' to each side of the equation.
5 + -5 + 6x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6x = 0 + -5
6x = 0 + -5

Combine like terms: 0 + -5 = -5
6x = -5

Divide each side by '6'.
x = -0.8333333333

Simplifying
x = -0.8333333333
Solution
x = {0, -0.8333333333}

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