x^2-5x+33=7x-2

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Solution for x^2-5x+33=7x-2 equation: 


Simplifying
x2 + -5x + 33 = 7x + -2

Reorder the terms:
33 + -5x + x2 = 7x + -2

Reorder the terms:
33 + -5x + x2 = -2 + 7x

Solving
33 + -5x + x2 = -2 + 7x

Solving for variable 'x'.

Reorder the terms:
33 + 2 + -5x + -7x + x2 = -2 + 7x + 2 + -7x

Combine like terms: 33 + 2 = 35
35 + -5x + -7x + x2 = -2 + 7x + 2 + -7x

Combine like terms: -5x + -7x = -12x
35 + -12x + x2 = -2 + 7x + 2 + -7x

Reorder the terms:
35 + -12x + x2 = -2 + 2 + 7x + -7x

Combine like terms: -2 + 2 = 0
35 + -12x + x2 = 0 + 7x + -7x
35 + -12x + x2 = 7x + -7x

Combine like terms: 7x + -7x = 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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