x^2-10x+43=5x-1

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Solution for x^2-10x+43=5x-1 equation: 


Simplifying
x2 + -10x + 43 = 5x + -1

Reorder the terms:
43 + -10x + x2 = 5x + -1

Reorder the terms:
43 + -10x + x2 = -1 + 5x

Solving
43 + -10x + x2 = -1 + 5x

Solving for variable 'x'.

Reorder the terms:
43 + 1 + -10x + -5x + x2 = -1 + 5x + 1 + -5x

Combine like terms: 43 + 1 = 44
44 + -10x + -5x + x2 = -1 + 5x + 1 + -5x

Combine like terms: -10x + -5x = -15x
44 + -15x + x2 = -1 + 5x + 1 + -5x

Reorder the terms:
44 + -15x + x2 = -1 + 1 + 5x + -5x

Combine like terms: -1 + 1 = 0
44 + -15x + x2 = 0 + 5x + -5x
44 + -15x + x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
44 + -15x + x2 = 0

Factor a trinomial.
(4 + -1x)(11 + -1x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

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

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

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {4, 11}

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