x*x-17x+43=-5x+8

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Solution for x*x-17x+43=-5x+8 equation: 


Simplifying
x * x + -17x + 43 = -5x + 8

Multiply x * x
x2 + -17x + 43 = -5x + 8

Reorder the terms:
43 + -17x + x2 = -5x + 8

Reorder the terms:
43 + -17x + x2 = 8 + -5x

Solving
43 + -17x + x2 = 8 + -5x

Solving for variable 'x'.

Reorder the terms:
43 + -8 + -17x + 5x + x2 = 8 + -5x + -8 + 5x

Combine like terms: 43 + -8 = 35
35 + -17x + 5x + x2 = 8 + -5x + -8 + 5x

Combine like terms: -17x + 5x = -12x
35 + -12x + x2 = 8 + -5x + -8 + 5x

Reorder the terms:
35 + -12x + x2 = 8 + -8 + -5x + 5x

Combine like terms: 8 + -8 = 0
35 + -12x + x2 = 0 + -5x + 5x
35 + -12x + x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
35 + -12x + 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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