x^2-4x+10=3x-2

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Solution for x^2-4x+10=3x-2 equation: 


Simplifying
x2 + -4x + 10 = 3x + -2

Reorder the terms:
10 + -4x + x2 = 3x + -2

Reorder the terms:
10 + -4x + x2 = -2 + 3x

Solving
10 + -4x + x2 = -2 + 3x

Solving for variable 'x'.

Reorder the terms:
10 + 2 + -4x + -3x + x2 = -2 + 3x + 2 + -3x

Combine like terms: 10 + 2 = 12
12 + -4x + -3x + x2 = -2 + 3x + 2 + -3x

Combine like terms: -4x + -3x = -7x
12 + -7x + x2 = -2 + 3x + 2 + -3x

Reorder the terms:
12 + -7x + x2 = -2 + 2 + 3x + -3x

Combine like terms: -2 + 2 = 0
12 + -7x + x2 = 0 + 3x + -3x
12 + -7x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
12 + -7x + x2 = 0

Factor a trinomial.
(3 + -1x)(4 + -1x) = 0


Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3

Subproblem 2
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
Solution
x = {3, 4}

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