3x(2+x)=x(3+-2)-24

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Solution for 3x(2+x)=x(3+-2)-24 equation: 


Simplifying
3x(2 + x) = x(3 + -2) + -24
(2 * 3x + x * 3x) = x(3 + -2) + -24
(6x + 3x2) = x(3 + -2) + -24

Combine like terms: 3 + -2 = 1
6x + 3x2 = x(1) + -24

Reorder the terms for easier multiplication:
6x + 3x2 = 1x + -24

Reorder the terms:
6x + 3x2 = -24 + 1x

Solving
6x + 3x2 = -24 + 1x

Solving for variable 'x'.

Reorder the terms:
24 + 6x + -1x + 3x2 = -24 + 1x + 24 + -1x

Combine like terms: 6x + -1x = 5x
24 + 5x + 3x2 = -24 + 1x + 24 + -1x

Reorder the terms:
24 + 5x + 3x2 = -24 + 24 + 1x + -1x

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

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

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

Divide each side by '3'.
8 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 1.666666667x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 1.666666667x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 1.666666667x + x2 = 0 + -8
1.666666667x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
1.666666667x + x2 = -8

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = -8 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = -8 + 0.6944444447

Combine like terms: -8 + 0.6944444447 = -7.3055555553
0.6944444447 + 1.666666667x + x2 = -7.3055555553

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = -7.3055555553

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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