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

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


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

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

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

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

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

Solving
-6 + 5x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-3 + -2x)(2 + -3x) = 0


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

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 = {-1.5, 0.6666666667}

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