2x^2-12x+41=x^2-14x+49

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Solution for 2x^2-12x+41=x^2-14x+49 equation: 


Simplifying
2x2 + -12x + 41 = x2 + -14x + 49

Reorder the terms:
41 + -12x + 2x2 = x2 + -14x + 49

Reorder the terms:
41 + -12x + 2x2 = 49 + -14x + x2

Solving
41 + -12x + 2x2 = 49 + -14x + x2

Solving for variable 'x'.

Reorder the terms:
41 + -49 + -12x + 14x + 2x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: 41 + -49 = -8
-8 + -12x + 14x + 2x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: -12x + 14x = 2x
-8 + 2x + 2x2 + -1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-8 + 2x + 1x2 = 49 + -14x + x2 + -49 + 14x + -1x2

Reorder the terms:
-8 + 2x + 1x2 = 49 + -49 + -14x + 14x + x2 + -1x2

Combine like terms: 49 + -49 = 0
-8 + 2x + 1x2 = 0 + -14x + 14x + x2 + -1x2
-8 + 2x + 1x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
-8 + 2x + 1x2 = 0 + x2 + -1x2
-8 + 2x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-8 + 2x + 1x2 = 0

Factor a trinomial.
(-4 + -1x)(2 + -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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-4, 2}

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