x^2-10x+38=4x-2

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Solution for x^2-10x+38=4x-2 equation: 


Simplifying
x2 + -10x + 38 = 4x + -2

Reorder the terms:
38 + -10x + x2 = 4x + -2

Reorder the terms:
38 + -10x + x2 = -2 + 4x

Solving
38 + -10x + x2 = -2 + 4x

Solving for variable 'x'.

Reorder the terms:
38 + 2 + -10x + -4x + x2 = -2 + 4x + 2 + -4x

Combine like terms: 38 + 2 = 40
40 + -10x + -4x + x2 = -2 + 4x + 2 + -4x

Combine like terms: -10x + -4x = -14x
40 + -14x + x2 = -2 + 4x + 2 + -4x

Reorder the terms:
40 + -14x + x2 = -2 + 2 + 4x + -4x

Combine like terms: -2 + 2 = 0
40 + -14x + x2 = 0 + 4x + -4x
40 + -14x + x2 = 4x + -4x

Combine like terms: 4x + -4x = 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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