x^2-17x+53=-3x+13

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Solution for x^2-17x+53=-3x+13 equation: 


Simplifying
x2 + -17x + 53 = -3x + 13

Reorder the terms:
53 + -17x + x2 = -3x + 13

Reorder the terms:
53 + -17x + x2 = 13 + -3x

Solving
53 + -17x + x2 = 13 + -3x

Solving for variable 'x'.

Reorder the terms:
53 + -13 + -17x + 3x + x2 = 13 + -3x + -13 + 3x

Combine like terms: 53 + -13 = 40
40 + -17x + 3x + x2 = 13 + -3x + -13 + 3x

Combine like terms: -17x + 3x = -14x
40 + -14x + x2 = 13 + -3x + -13 + 3x

Reorder the terms:
40 + -14x + x2 = 13 + -13 + -3x + 3x

Combine like terms: 13 + -13 = 0
40 + -14x + x2 = 0 + -3x + 3x
40 + -14x + x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
40 + -14x + x2 = 0

Factor a trinomial.
(4 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {4, 10}

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