12-3x^2-48=24x+96

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Solution for 12-3x^2-48=24x+96 equation: 


Simplifying
12 + -3x2 + -48 = 24x + 96

Reorder the terms:
12 + -48 + -3x2 = 24x + 96

Combine like terms: 12 + -48 = -36
-36 + -3x2 = 24x + 96

Reorder the terms:
-36 + -3x2 = 96 + 24x

Solving
-36 + -3x2 = 96 + 24x

Solving for variable 'x'.

Reorder the terms:
-36 + -96 + -24x + -3x2 = 96 + 24x + -96 + -24x

Combine like terms: -36 + -96 = -132
-132 + -24x + -3x2 = 96 + 24x + -96 + -24x

Reorder the terms:
-132 + -24x + -3x2 = 96 + -96 + 24x + -24x

Combine like terms: 96 + -96 = 0
-132 + -24x + -3x2 = 0 + 24x + -24x
-132 + -24x + -3x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
-132 + -24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(44 + 8x + x2) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(44 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
44 + 8x + x2 = 0

Solving
44 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-44' to each side of the equation.
44 + 8x + -44 + x2 = 0 + -44

Reorder the terms:
44 + -44 + 8x + x2 = 0 + -44

Combine like terms: 44 + -44 = 0
0 + 8x + x2 = 0 + -44
8x + x2 = 0 + -44

Combine like terms: 0 + -44 = -44
8x + x2 = -44

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = -44 + 16

Reorder the terms:
16 + 8x + x2 = -44 + 16

Combine like terms: -44 + 16 = -28
16 + 8x + x2 = -28

Factor a perfect square on the left side:
(x + 4)(x + 4) = -28

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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