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

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


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

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

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

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

Reorder the terms:
9 + -3x + -2x2 + -1(3 + -2x)(-1x + -2) = 0

Reorder the terms:
9 + -3x + -2x2 + -1(3 + -2x)(-2 + -1x) = 0

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

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

Reorder the terms:
9 + 6 + -3x + -1x + -2x2 + -2x2 = 0

Combine like terms: 9 + 6 = 15
15 + -3x + -1x + -2x2 + -2x2 = 0

Combine like terms: -3x + -1x = -4x
15 + -4x + -2x2 + -2x2 = 0

Combine like terms: -2x2 + -2x2 = -4x2
15 + -4x + -4x2 = 0

Solving
15 + -4x + -4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -2x)(5 + 2x) = 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 '(5 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {1.5, -2.5}

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