4x^2-3x+8+6x-5x^2-32=0

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Solution for 4x^2-3x+8+6x-5x^2-32=0 equation:


Simplifying
4x2 + -3x + 8 + 6x + -5x2 + -32 = 0

Reorder the terms:
8 + -32 + -3x + 6x + 4x2 + -5x2 = 0

Combine like terms: 8 + -32 = -24
-24 + -3x + 6x + 4x2 + -5x2 = 0

Combine like terms: -3x + 6x = 3x
-24 + 3x + 4x2 + -5x2 = 0

Combine like terms: 4x2 + -5x2 = -1x2
-24 + 3x + -1x2 = 0

Solving
-24 + 3x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
24 + -3x + x2 = 0

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -3x + -24 + x2 = 0 + -24

Reorder the terms:
24 + -24 + -3x + x2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -3x + x2 = 0 + -24
-3x + x2 = 0 + -24

Combine like terms: 0 + -24 = -24
-3x + x2 = -24

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -24 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -24 + 2.25

Combine like terms: -24 + 2.25 = -21.75
2.25 + -3x + x2 = -21.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -21.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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