4(x^2-24x+144)=-204

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Solution for 4(x^2-24x+144)=-204 equation: 


Simplifying
4(x2 + -24x + 144) = -204

Reorder the terms:
4(144 + -24x + x2) = -204
(144 * 4 + -24x * 4 + x2 * 4) = -204
(576 + -96x + 4x2) = -204

Solving
576 + -96x + 4x2 = -204

Solving for variable 'x'.

Reorder the terms:
576 + 204 + -96x + 4x2 = -204 + 204

Combine like terms: 576 + 204 = 780
780 + -96x + 4x2 = -204 + 204

Combine like terms: -204 + 204 = 0
780 + -96x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(195 + -24x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(195 + -24x + x2)' equal to zero and attempt to solve:

Simplifying
195 + -24x + x2 = 0

Solving
195 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-195' to each side of the equation.
195 + -24x + -195 + x2 = 0 + -195

Reorder the terms:
195 + -195 + -24x + x2 = 0 + -195

Combine like terms: 195 + -195 = 0
0 + -24x + x2 = 0 + -195
-24x + x2 = 0 + -195

Combine like terms: 0 + -195 = -195
-24x + x2 = -195

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -195 + 144

Reorder the terms:
144 + -24x + x2 = -195 + 144

Combine like terms: -195 + 144 = -51
144 + -24x + x2 = -51

Factor a perfect square on the left side:
(x + -12)(x + -12) = -51

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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