x^2-1x-40=x-5

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Solution for x^2-1x-40=x-5 equation: 


Simplifying
x2 + -1x + -40 = x + -5

Reorder the terms:
-40 + -1x + x2 = x + -5

Reorder the terms:
-40 + -1x + x2 = -5 + x

Solving
-40 + -1x + x2 = -5 + x

Solving for variable 'x'.

Reorder the terms:
-40 + 5 + -1x + -1x + x2 = -5 + x + 5 + -1x

Combine like terms: -40 + 5 = -35
-35 + -1x + -1x + x2 = -5 + x + 5 + -1x

Combine like terms: -1x + -1x = -2x
-35 + -2x + x2 = -5 + x + 5 + -1x

Reorder the terms:
-35 + -2x + x2 = -5 + 5 + x + -1x

Combine like terms: -5 + 5 = 0
-35 + -2x + x2 = 0 + x + -1x
-35 + -2x + x2 = x + -1x

Combine like terms: x + -1x = 0
-35 + -2x + x2 = 0

Factor a trinomial.
(-5 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-5, 7}

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