X^2-4X+89=2X^2+X-15

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Solution for X^2-4X+89=2X^2+X-15 equation: 


Simplifying
X2 + -4X + 89 = 2X2 + X + -15

Reorder the terms:
89 + -4X + X2 = 2X2 + X + -15

Reorder the terms:
89 + -4X + X2 = -15 + X + 2X2

Solving
89 + -4X + X2 = -15 + X + 2X2

Solving for variable 'X'.

Reorder the terms:
89 + 15 + -4X + -1X + X2 + -2X2 = -15 + X + 2X2 + 15 + -1X + -2X2

Combine like terms: 89 + 15 = 104
104 + -4X + -1X + X2 + -2X2 = -15 + X + 2X2 + 15 + -1X + -2X2

Combine like terms: -4X + -1X = -5X
104 + -5X + X2 + -2X2 = -15 + X + 2X2 + 15 + -1X + -2X2

Combine like terms: X2 + -2X2 = -1X2
104 + -5X + -1X2 = -15 + X + 2X2 + 15 + -1X + -2X2

Reorder the terms:
104 + -5X + -1X2 = -15 + 15 + X + -1X + 2X2 + -2X2

Combine like terms: -15 + 15 = 0
104 + -5X + -1X2 = 0 + X + -1X + 2X2 + -2X2
104 + -5X + -1X2 = X + -1X + 2X2 + -2X2

Combine like terms: X + -1X = 0
104 + -5X + -1X2 = 0 + 2X2 + -2X2
104 + -5X + -1X2 = 2X2 + -2X2

Combine like terms: 2X2 + -2X2 = 0
104 + -5X + -1X2 = 0

Factor a trinomial.
(8 + -1X)(13 + X) = 0


Subproblem 1
Set the factor '(8 + -1X)' equal to zero and attempt to solve:

Simplifying
8 + -1X = 0

Solving
8 + -1X = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1X = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1X = 0 + -8
-1X = 0 + -8

Combine like terms: 0 + -8 = -8
-1X = -8

Divide each side by '-1'.
X = 8

Simplifying
X = 8

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 = {8, -13}

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