85+(X^2+1)=2X^2+6X-5

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Solution for 85+(X^2+1)=2X^2+6X-5 equation: 


Simplifying
85 + (X2 + 1) = 2X2 + 6X + -5

Reorder the terms:
85 + (1 + X2) = 2X2 + 6X + -5

Remove parenthesis around (1 + X2)
85 + 1 + X2 = 2X2 + 6X + -5

Combine like terms: 85 + 1 = 86
86 + X2 = 2X2 + 6X + -5

Reorder the terms:
86 + X2 = -5 + 6X + 2X2

Solving
86 + X2 = -5 + 6X + 2X2

Solving for variable 'X'.

Reorder the terms:
86 + 5 + -6X + X2 + -2X2 = -5 + 6X + 2X2 + 5 + -6X + -2X2

Combine like terms: 86 + 5 = 91
91 + -6X + X2 + -2X2 = -5 + 6X + 2X2 + 5 + -6X + -2X2

Combine like terms: X2 + -2X2 = -1X2
91 + -6X + -1X2 = -5 + 6X + 2X2 + 5 + -6X + -2X2

Reorder the terms:
91 + -6X + -1X2 = -5 + 5 + 6X + -6X + 2X2 + -2X2

Combine like terms: -5 + 5 = 0
91 + -6X + -1X2 = 0 + 6X + -6X + 2X2 + -2X2
91 + -6X + -1X2 = 6X + -6X + 2X2 + -2X2

Combine like terms: 6X + -6X = 0
91 + -6X + -1X2 = 0 + 2X2 + -2X2
91 + -6X + -1X2 = 2X2 + -2X2

Combine like terms: 2X2 + -2X2 = 0
91 + -6X + -1X2 = 0

Factor a trinomial.
(7 + -1X)(13 + X) = 0


Subproblem 1
Set the factor '(7 + -1X)' equal to zero and attempt to solve:

Simplifying
7 + -1X = 0

Solving
7 + -1X = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1X = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1X = 0 + -7
-1X = 0 + -7

Combine like terms: 0 + -7 = -7
-1X = -7

Divide each side by '-1'.
X = 7

Simplifying
X = 7

Subproblem 2
Set the factor '(13 + X)' equal to zero and attempt to solve:

Simplifying
13 + X = 0

Solving
13 + X = 0

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

Add '-13' to each side of the equation.
13 + -13 + X = 0 + -13

Combine like terms: 13 + -13 = 0
0 + X = 0 + -13
X = 0 + -13

Combine like terms: 0 + -13 = -13
X = -13

Simplifying
X = -13
Solution
X = {7, -13}

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