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

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


Simplifying
(2x + -3) + -1(3x + 2)(2x + -3) = 0

Reorder the terms:
(-3 + 2x) + -1(3x + 2)(2x + -3) = 0

Remove parenthesis around (-3 + 2x)
-3 + 2x + -1(3x + 2)(2x + -3) = 0

Reorder the terms:
-3 + 2x + -1(2 + 3x)(2x + -3) = 0

Reorder the terms:
-3 + 2x + -1(2 + 3x)(-3 + 2x) = 0

Multiply (2 + 3x) * (-3 + 2x)
-3 + 2x + -1(2(-3 + 2x) + 3x * (-3 + 2x)) = 0
-3 + 2x + -1((-3 * 2 + 2x * 2) + 3x * (-3 + 2x)) = 0
-3 + 2x + -1((-6 + 4x) + 3x * (-3 + 2x)) = 0
-3 + 2x + -1(-6 + 4x + (-3 * 3x + 2x * 3x)) = 0
-3 + 2x + -1(-6 + 4x + (-9x + 6x2)) = 0

Combine like terms: 4x + -9x = -5x
-3 + 2x + -1(-6 + -5x + 6x2) = 0
-3 + 2x + (-6 * -1 + -5x * -1 + 6x2 * -1) = 0
-3 + 2x + (6 + 5x + -6x2) = 0

Reorder the terms:
-3 + 6 + 2x + 5x + -6x2 = 0

Combine like terms: -3 + 6 = 3
3 + 2x + 5x + -6x2 = 0

Combine like terms: 2x + 5x = 7x
3 + 7x + -6x2 = 0

Solving
3 + 7x + -6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -2x)(1 + 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 '(1 + 3x)' equal to zero and attempt to solve:

Simplifying
1 + 3x = 0

Solving
1 + 3x = 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 + 3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3x = 0 + -1
3x = 0 + -1

Combine like terms: 0 + -1 = -1
3x = -1

Divide each side by '3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
Solution
x = {1.5, -0.3333333333}

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