(-3X^2-8X+3)-(5x^2+3)=

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Solution for (-3X^2-8X+3)-(5x^2+3)= equation: 


Simplifying
(-3X2 + -8X + 3) + -1(5x2 + 3) = 0

Reorder the terms:
(3 + -8X + -3X2) + -1(5x2 + 3) = 0

Remove parenthesis around (3 + -8X + -3X2)
3 + -8X + -3X2 + -1(5x2 + 3) = 0

Reorder the terms:
3 + -8X + -3X2 + -1(3 + 5x2) = 0
3 + -8X + -3X2 + (3 * -1 + 5x2 * -1) = 0
3 + -8X + -3X2 + (-3 + -5x2) = 0

Reorder the terms:
3 + -3 + -8X + -3X2 + -5x2 = 0

Combine like terms: 3 + -3 = 0
0 + -8X + -3X2 + -5x2 = 0
-8X + -3X2 + -5x2 = 0

Solving
-8X + -3X2 + -5x2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(8X + 3X2 + 5x2) = 0

Factor a trinomial.
-1((X + x)(3X + 5x)) = 0

Ignore the factor -1.

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

Simplifying
X + x = 0

Solving
X + x = 0

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

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

Combine like terms: x + -1x = 0
X + 0 = 0 + -1x
X = 0 + -1x
Remove the zero:
X = -1x

Simplifying
X = -1x

Subproblem 2
Set the factor '(3X + 5x)' equal to zero and attempt to solve:

Simplifying
3X + 5x = 0

Solving
3X + 5x = 0

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

Add '-5x' to each side of the equation.
3X + 5x + -5x = 0 + -5x

Combine like terms: 5x + -5x = 0
3X + 0 = 0 + -5x
3X = 0 + -5x
Remove the zero:
3X = -5x

Divide each side by '3'.
X = -1.666666667x

Simplifying
X = -1.666666667x
Solution
X = {-1x, -1.666666667x}

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