x^2+24x=12x-15-3x^2

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Solution for x^2+24x=12x-15-3x^2 equation: 


Simplifying
x2 + 24x = 12x + -15 + -3x2

Reorder the terms:
24x + x2 = 12x + -15 + -3x2

Reorder the terms:
24x + x2 = -15 + 12x + -3x2

Solving
24x + x2 = -15 + 12x + -3x2

Solving for variable 'x'.

Reorder the terms:
15 + 24x + -12x + x2 + 3x2 = -15 + 12x + -3x2 + 15 + -12x + 3x2

Combine like terms: 24x + -12x = 12x
15 + 12x + x2 + 3x2 = -15 + 12x + -3x2 + 15 + -12x + 3x2

Combine like terms: x2 + 3x2 = 4x2
15 + 12x + 4x2 = -15 + 12x + -3x2 + 15 + -12x + 3x2

Reorder the terms:
15 + 12x + 4x2 = -15 + 15 + 12x + -12x + -3x2 + 3x2

Combine like terms: -15 + 15 = 0
15 + 12x + 4x2 = 0 + 12x + -12x + -3x2 + 3x2
15 + 12x + 4x2 = 12x + -12x + -3x2 + 3x2

Combine like terms: 12x + -12x = 0
15 + 12x + 4x2 = 0 + -3x2 + 3x2
15 + 12x + 4x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
15 + 12x + 4x2 = 0

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

Divide each side by '4'.
3.75 + 3x + x2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + 3x + -3.75 + x2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + 3x + x2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + 3x + x2 = 0 + -3.75
3x + x2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
3x + x2 = -3.75

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 = -3.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -3.75 + 2.25

Combine like terms: -3.75 + 2.25 = -1.5
2.25 + 3x + x2 = -1.5

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

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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