12-3x^2-48=24x+72

Solution for 12-3x^2-48=24x+72 equation:

Simplifying
12 + -3x2 + -48 = 24x + 72

Reorder the terms:
12 + -48 + -3x2 = 24x + 72

Combine like terms: 12 + -48 = -36
-36 + -3x2 = 24x + 72

Reorder the terms:
-36 + -3x2 = 72 + 24x

Solving
-36 + -3x2 = 72 + 24x

Solving for variable 'x'.

Reorder the terms:
-36 + -72 + -24x + -3x2 = 72 + 24x + -72 + -24x

Combine like terms: -36 + -72 = -108
-108 + -24x + -3x2 = 72 + 24x + -72 + -24x

Reorder the terms:
-108 + -24x + -3x2 = 72 + -72 + 24x + -24x

Combine like terms: 72 + -72 = 0
-108 + -24x + -3x2 = 0 + 24x + -24x
-108 + -24x + -3x2 = 24x + -24x

Combine like terms: 24x + -24x = 0
-108 + -24x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(36 + 8x + x2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(36 + 8x + x2)' equal to zero and attempt to solve:

Simplifying
36 + 8x + x2 = 0

Solving
36 + 8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 8x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + 8x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 8x + x2 = 0 + -36
8x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
8x + x2 = -36

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 = -36 + 16

Reorder the terms:
16 + 8x + x2 = -36 + 16

Combine like terms: -36 + 16 = -20
16 + 8x + x2 = -20

Factor a perfect square on the left side:
(x + 4)(x + 4) = -20

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.