2x^2+50=x^2+4x+110

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Solution for 2x^2+50=x^2+4x+110 equation: 


Simplifying
2x2 + 50 = x2 + 4x + 110

Reorder the terms:
50 + 2x2 = x2 + 4x + 110

Reorder the terms:
50 + 2x2 = 110 + 4x + x2

Solving
50 + 2x2 = 110 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
50 + -110 + -4x + 2x2 + -1x2 = 110 + 4x + x2 + -110 + -4x + -1x2

Combine like terms: 50 + -110 = -60
-60 + -4x + 2x2 + -1x2 = 110 + 4x + x2 + -110 + -4x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-60 + -4x + 1x2 = 110 + 4x + x2 + -110 + -4x + -1x2

Reorder the terms:
-60 + -4x + 1x2 = 110 + -110 + 4x + -4x + x2 + -1x2

Combine like terms: 110 + -110 = 0
-60 + -4x + 1x2 = 0 + 4x + -4x + x2 + -1x2
-60 + -4x + 1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
-60 + -4x + 1x2 = 0 + x2 + -1x2
-60 + -4x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-60 + -4x + 1x2 = 0

Factor a trinomial.
(-6 + -1x)(10 + -1x) = 0


Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

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 = {-6, 10}

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