(x-1)(x-2)=x+47

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Solution for (x-1)(x-2)=x+47 equation: 


Simplifying
(x + -1)(x + -2) = x + 47

Reorder the terms:
(-1 + x)(x + -2) = x + 47

Reorder the terms:
(-1 + x)(-2 + x) = x + 47

Multiply (-1 + x) * (-2 + x)
(-1(-2 + x) + x(-2 + x)) = x + 47
((-2 * -1 + x * -1) + x(-2 + x)) = x + 47
((2 + -1x) + x(-2 + x)) = x + 47
(2 + -1x + (-2 * x + x * x)) = x + 47
(2 + -1x + (-2x + x2)) = x + 47

Combine like terms: -1x + -2x = -3x
(2 + -3x + x2) = x + 47

Reorder the terms:
2 + -3x + x2 = 47 + x

Solving
2 + -3x + x2 = 47 + x

Solving for variable 'x'.

Reorder the terms:
2 + -47 + -3x + -1x + x2 = 47 + x + -47 + -1x

Combine like terms: 2 + -47 = -45
-45 + -3x + -1x + x2 = 47 + x + -47 + -1x

Combine like terms: -3x + -1x = -4x
-45 + -4x + x2 = 47 + x + -47 + -1x

Reorder the terms:
-45 + -4x + x2 = 47 + -47 + x + -1x

Combine like terms: 47 + -47 = 0
-45 + -4x + x2 = 0 + x + -1x
-45 + -4x + x2 = x + -1x

Combine like terms: x + -1x = 0
-45 + -4x + x2 = 0

Factor a trinomial.
(-5 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-5, 9}

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