x^4-(4a+12)x^2+12a+27=0

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Solution for x^4-(4a+12)x^2+12a+27=0 equation: 


Simplifying
x4 + -1(4a + 12) * x2 + 12a + 27 = 0

Reorder the terms:
x4 + -1(12 + 4a) * x2 + 12a + 27 = 0

Reorder the terms for easier multiplication:
x4 + -1x2(12 + 4a) + 12a + 27 = 0
x4 + (12 * -1x2 + 4a * -1x2) + 12a + 27 = 0

Reorder the terms:
x4 + (-4ax2 + -12x2) + 12a + 27 = 0
x4 + (-4ax2 + -12x2) + 12a + 27 = 0

Reorder the terms:
27 + 12a + -4ax2 + -12x2 + x4 = 0

Solving
27 + 12a + -4ax2 + -12x2 + x4 = 0

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-27' to each side of the equation.
27 + 12a + -4ax2 + -12x2 + -27 + x4 = 0 + -27

Reorder the terms:
27 + -27 + 12a + -4ax2 + -12x2 + x4 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 12a + -4ax2 + -12x2 + x4 = 0 + -27
12a + -4ax2 + -12x2 + x4 = 0 + -27

Combine like terms: 0 + -27 = -27
12a + -4ax2 + -12x2 + x4 = -27

Add '12x2' to each side of the equation.
12a + -4ax2 + -12x2 + 12x2 + x4 = -27 + 12x2

Combine like terms: -12x2 + 12x2 = 0
12a + -4ax2 + 0 + x4 = -27 + 12x2
12a + -4ax2 + x4 = -27 + 12x2

Add '-1x4' to each side of the equation.
12a + -4ax2 + x4 + -1x4 = -27 + 12x2 + -1x4

Combine like terms: x4 + -1x4 = 0
12a + -4ax2 + 0 = -27 + 12x2 + -1x4
12a + -4ax2 = -27 + 12x2 + -1x4

Reorder the terms:
27 + 12a + -4ax2 + -12x2 + x4 = -27 + 12x2 + -1x4 + 27 + -12x2 + x4

Reorder the terms:
27 + 12a + -4ax2 + -12x2 + x4 = -27 + 27 + 12x2 + -12x2 + -1x4 + x4

Combine like terms: -27 + 27 = 0
27 + 12a + -4ax2 + -12x2 + x4 = 0 + 12x2 + -12x2 + -1x4 + x4
27 + 12a + -4ax2 + -12x2 + x4 = 12x2 + -12x2 + -1x4 + x4

Combine like terms: 12x2 + -12x2 = 0
27 + 12a + -4ax2 + -12x2 + x4 = 0 + -1x4 + x4
27 + 12a + -4ax2 + -12x2 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
27 + 12a + -4ax2 + -12x2 + x4 = 0

The solution to this equation could not be determined.

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