0=-3x^2+24x-54

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Solution for 0=-3x^2+24x-54 equation: 


Simplifying
0 = -3x2 + 24x + -54

Reorder the terms:
0 = -54 + 24x + -3x2

Solving
0 = -54 + 24x + -3x2

Solving for variable 'x'.

Combine like terms: 0 + 54 = 54
54 + -24x + 3x2 = -54 + 24x + -3x2 + 54 + -24x + 3x2

Reorder the terms:
54 + -24x + 3x2 = -54 + 54 + 24x + -24x + -3x2 + 3x2

Combine like terms: -54 + 54 = 0
54 + -24x + 3x2 = 0 + 24x + -24x + -3x2 + 3x2
54 + -24x + 3x2 = 24x + -24x + -3x2 + 3x2

Combine like terms: 24x + -24x = 0
54 + -24x + 3x2 = 0 + -3x2 + 3x2
54 + -24x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
54 + -24x + 3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(18 + -8x + x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(18 + -8x + x2)' equal to zero and attempt to solve:

Simplifying
18 + -8x + x2 = 0

Solving
18 + -8x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + -8x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + -8x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -8x + x2 = 0 + -18
-8x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
-8x + x2 = -18

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 = -18 + 16

Reorder the terms:
16 + -8x + x2 = -18 + 16

Combine like terms: -18 + 16 = -2
16 + -8x + x2 = -2

Factor a perfect square on the left side:
(x + -4)(x + -4) = -2

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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