(2x-3)(-x-2)=(x-1)(2x-3)

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Solution for (2x-3)(-x-2)=(x-1)(2x-3) equation: 


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

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

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

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

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

Reorder the terms:
6 + -1x + -2x2 = (-1 + x)(2x + -3)

Reorder the terms:
6 + -1x + -2x2 = (-1 + x)(-3 + 2x)

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

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

Solving
6 + -1x + -2x2 = 3 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
6 + -3 + -1x + 5x + -2x2 + -2x2 = 3 + -5x + 2x2 + -3 + 5x + -2x2

Combine like terms: 6 + -3 = 3
3 + -1x + 5x + -2x2 + -2x2 = 3 + -5x + 2x2 + -3 + 5x + -2x2

Combine like terms: -1x + 5x = 4x
3 + 4x + -2x2 + -2x2 = 3 + -5x + 2x2 + -3 + 5x + -2x2

Combine like terms: -2x2 + -2x2 = -4x2
3 + 4x + -4x2 = 3 + -5x + 2x2 + -3 + 5x + -2x2

Reorder the terms:
3 + 4x + -4x2 = 3 + -3 + -5x + 5x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
3 + 4x + -4x2 = 0 + -5x + 5x + 2x2 + -2x2
3 + 4x + -4x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
3 + 4x + -4x2 = 0 + 2x2 + -2x2
3 + 4x + -4x2 = 2x2 + -2x2

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

Factor a trinomial.
(3 + -2x)(1 + 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 '(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 = {1.5, -0.5}

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