(2x-4)(x+1)=(x-3)(x-2)

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Solution for (2x-4)(x+1)=(x-3)(x-2) equation: 


Simplifying
(2x + -4)(x + 1) = (x + -3)(x + -2)

Reorder the terms:
(-4 + 2x)(x + 1) = (x + -3)(x + -2)

Reorder the terms:
(-4 + 2x)(1 + x) = (x + -3)(x + -2)

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

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

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

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

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

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

Solving
-4 + -2x + 2x2 = 6 + -5x + x2

Solving for variable 'x'.

Reorder the terms:
-4 + -6 + -2x + 5x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Combine like terms: -4 + -6 = -10
-10 + -2x + 5x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Combine like terms: -2x + 5x = 3x
-10 + 3x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-10 + 3x + 1x2 = 6 + -5x + x2 + -6 + 5x + -1x2

Reorder the terms:
-10 + 3x + 1x2 = 6 + -6 + -5x + 5x + x2 + -1x2

Combine like terms: 6 + -6 = 0
-10 + 3x + 1x2 = 0 + -5x + 5x + x2 + -1x2
-10 + 3x + 1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
-10 + 3x + 1x2 = 0 + x2 + -1x2
-10 + 3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 3x + 1x2 = 0

Factor a trinomial.
(-5 + -1x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1x = 0 + 5
-1x = 0 + 5

Combine like terms: 0 + 5 = 5
-1x = 5

Divide each side by '-1'.
x = -5

Simplifying
x = -5

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-5, 2}

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