x^2-12x+42=3x-2

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Solution for x^2-12x+42=3x-2 equation: 


Simplifying
x2 + -12x + 42 = 3x + -2

Reorder the terms:
42 + -12x + x2 = 3x + -2

Reorder the terms:
42 + -12x + x2 = -2 + 3x

Solving
42 + -12x + x2 = -2 + 3x

Solving for variable 'x'.

Reorder the terms:
42 + 2 + -12x + -3x + x2 = -2 + 3x + 2 + -3x

Combine like terms: 42 + 2 = 44
44 + -12x + -3x + x2 = -2 + 3x + 2 + -3x

Combine like terms: -12x + -3x = -15x
44 + -15x + x2 = -2 + 3x + 2 + -3x

Reorder the terms:
44 + -15x + x2 = -2 + 2 + 3x + -3x

Combine like terms: -2 + 2 = 0
44 + -15x + x2 = 0 + 3x + -3x
44 + -15x + x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
44 + -15x + x2 = 0

Factor a trinomial.
(4 + -1x)(11 + -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 '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {4, 11}

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