(-2X^2-3X+1)+(3X^2+5X-4)=0

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Solution for (-2X^2-3X+1)+(3X^2+5X-4)=0 equation: 


Simplifying
(-2X2 + -3X + 1) + (3X2 + 5X + -4) = 0

Reorder the terms:
(1 + -3X + -2X2) + (3X2 + 5X + -4) = 0

Remove parenthesis around (1 + -3X + -2X2)
1 + -3X + -2X2 + (3X2 + 5X + -4) = 0

Reorder the terms:
1 + -3X + -2X2 + (-4 + 5X + 3X2) = 0

Remove parenthesis around (-4 + 5X + 3X2)
1 + -3X + -2X2 + -4 + 5X + 3X2 = 0

Reorder the terms:
1 + -4 + -3X + 5X + -2X2 + 3X2 = 0

Combine like terms: 1 + -4 = -3
-3 + -3X + 5X + -2X2 + 3X2 = 0

Combine like terms: -3X + 5X = 2X
-3 + 2X + -2X2 + 3X2 = 0

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

Solving
-3 + 2X + 1X2 = 0

Solving for variable 'X'.

Factor a trinomial.
(-3 + -1X)(1 + -1X) = 0


Subproblem 1
Set the factor '(-3 + -1X)' equal to zero and attempt to solve:

Simplifying
-3 + -1X = 0

Solving
-3 + -1X = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1X = 0 + 3

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

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

Divide each side by '-1'.
X = -3

Simplifying
X = -3

Subproblem 2
Set the factor '(1 + -1X)' equal to zero and attempt to solve:

Simplifying
1 + -1X = 0

Solving
1 + -1X = 0

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

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

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

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

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

Simplifying
X = 1
Solution
X = {-3, 1}

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