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

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


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

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

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

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

Combine like terms: 2x + -2x = 0
(-4 + 0 + x2) = (2x + 1)(x + -2)
(-4 + x2) = (2x + 1)(x + -2)

Reorder the terms:
-4 + x2 = (1 + 2x)(x + -2)

Reorder the terms:
-4 + x2 = (1 + 2x)(-2 + x)

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

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

Solving
-4 + x2 = -2 + -3x + 2x2

Solving for variable 'x'.

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

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

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

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

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

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

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

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


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

Simplifying
-2 + x = 0

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

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

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

Simplifying
x = 2

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {2, 1}

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