2X^2=3X^2-2X-8

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Solution for 2X^2=3X^2-2X-8 equation: 


Simplifying
2X2 = 3X2 + -2X + -8

Reorder the terms:
2X2 = -8 + -2X + 3X2

Solving
2X2 = -8 + -2X + 3X2

Solving for variable 'X'.

Reorder the terms:
8 + 2X + 2X2 + -3X2 = -8 + -2X + 3X2 + 8 + 2X + -3X2

Combine like terms: 2X2 + -3X2 = -1X2
8 + 2X + -1X2 = -8 + -2X + 3X2 + 8 + 2X + -3X2

Reorder the terms:
8 + 2X + -1X2 = -8 + 8 + -2X + 2X + 3X2 + -3X2

Combine like terms: -8 + 8 = 0
8 + 2X + -1X2 = 0 + -2X + 2X + 3X2 + -3X2
8 + 2X + -1X2 = -2X + 2X + 3X2 + -3X2

Combine like terms: -2X + 2X = 0
8 + 2X + -1X2 = 0 + 3X2 + -3X2
8 + 2X + -1X2 = 3X2 + -3X2

Combine like terms: 3X2 + -3X2 = 0
8 + 2X + -1X2 = 0

Factor a trinomial.
(4 + -1X)(2 + X) = 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 + 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 = {4, -2}

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