(2X-1)+(X-3)=X^2-14

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Solution for (2X-1)+(X-3)=X^2-14 equation: 


Simplifying
(2X + -1) + (X + -3) = X2 + -14

Reorder the terms:
(-1 + 2X) + (X + -3) = X2 + -14

Remove parenthesis around (-1 + 2X)
-1 + 2X + (X + -3) = X2 + -14

Reorder the terms:
-1 + 2X + (-3 + X) = X2 + -14

Remove parenthesis around (-3 + X)
-1 + 2X + -3 + X = X2 + -14

Reorder the terms:
-1 + -3 + 2X + X = X2 + -14

Combine like terms: -1 + -3 = -4
-4 + 2X + X = X2 + -14

Combine like terms: 2X + X = 3X
-4 + 3X = X2 + -14

Reorder the terms:
-4 + 3X = -14 + X2

Solving
-4 + 3X = -14 + X2

Solving for variable 'X'.

Reorder the terms:
-4 + 14 + 3X + -1X2 = -14 + X2 + 14 + -1X2

Combine like terms: -4 + 14 = 10
10 + 3X + -1X2 = -14 + X2 + 14 + -1X2

Reorder the terms:
10 + 3X + -1X2 = -14 + 14 + X2 + -1X2

Combine like terms: -14 + 14 = 0
10 + 3X + -1X2 = 0 + X2 + -1X2
10 + 3X + -1X2 = X2 + -1X2

Combine like terms: X2 + -1X2 = 0
10 + 3X + -1X2 = 0

Factor a trinomial.
(5 + -1X)(2 + X) = 0


Subproblem 1
Set the factor '(5 + -1X)' equal to zero and attempt to solve:

Simplifying
5 + -1X = 0

Solving
5 + -1X = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1X = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1X = 0 + -5
-1X = 0 + -5

Combine like terms: 0 + -5 = -5
-1X = -5

Divide each side by '-1'.
X = 5

Simplifying
X = 5

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

Simplifying
2 + X = 0

Solving
2 + X = 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 + X = 0 + -2

Combine like terms: 2 + -2 = 0
0 + X = 0 + -2
X = 0 + -2

Combine like terms: 0 + -2 = -2
X = -2

Simplifying
X = -2
Solution
X = {5, -2}

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