(x+1)(x+2)=7-x(2-x)

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Solution for (x+1)(x+2)=7-x(2-x) equation: 


Simplifying
(x + 1)(x + 2) = 7 + -1x(2 + -1x)

Reorder the terms:
(1 + x)(x + 2) = 7 + -1x(2 + -1x)

Reorder the terms:
(1 + x)(2 + x) = 7 + -1x(2 + -1x)

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) = 7 + -1x(2 + -1x)
((2 * 1 + x * 1) + x(2 + x)) = 7 + -1x(2 + -1x)
((2 + 1x) + x(2 + x)) = 7 + -1x(2 + -1x)
(2 + 1x + (2 * x + x * x)) = 7 + -1x(2 + -1x)
(2 + 1x + (2x + x2)) = 7 + -1x(2 + -1x)

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) = 7 + -1x(2 + -1x)
2 + 3x + x2 = 7 + (2 * -1x + -1x * -1x)
2 + 3x + x2 = 7 + (-2x + 1x2)

Solving
2 + 3x + x2 = 7 + -2x + 1x2

Solving for variable 'x'.

Reorder the terms:
2 + -7 + 3x + 2x + x2 + -1x2 = 7 + -2x + 1x2 + -7 + 2x + -1x2

Combine like terms: 2 + -7 = -5
-5 + 3x + 2x + x2 + -1x2 = 7 + -2x + 1x2 + -7 + 2x + -1x2

Combine like terms: 3x + 2x = 5x
-5 + 5x + x2 + -1x2 = 7 + -2x + 1x2 + -7 + 2x + -1x2

Combine like terms: x2 + -1x2 = 0
-5 + 5x + 0 = 7 + -2x + 1x2 + -7 + 2x + -1x2
-5 + 5x = 7 + -2x + 1x2 + -7 + 2x + -1x2

Reorder the terms:
-5 + 5x = 7 + -7 + -2x + 2x + 1x2 + -1x2

Combine like terms: 7 + -7 = 0
-5 + 5x = 0 + -2x + 2x + 1x2 + -1x2
-5 + 5x = -2x + 2x + 1x2 + -1x2

Combine like terms: -2x + 2x = 0
-5 + 5x = 0 + 1x2 + -1x2
-5 + 5x = 1x2 + -1x2

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

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + x) = 0

Ignore the factor 5.

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

Simplifying
-1 + x = 0

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

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

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

Simplifying
x = 1
Solution
x = {1}

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