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

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


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

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

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

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

Combine like terms: 9x + -4x = 5x
(-6 + 5x + 6x2) + 2 = 0

Reorder the terms:
-6 + 2 + 5x + 6x2 = 0

Combine like terms: -6 + 2 = -4
-4 + 5x + 6x2 = 0

Solving
-4 + 5x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-4 + -3x)(1 + -2x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Solution
x = {-1.333333333, 0.5}

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