30x^2-41x-10x-3x=-12-6+54-108

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Solution for 30x^2-41x-10x-3x=-12-6+54-108 equation: 


Simplifying
30x2 + -41x + -10x + -3x = -12 + -6 + 54 + -108

Reorder the terms:
-41x + -10x + -3x + 30x2 = -12 + -6 + 54 + -108

Combine like terms: -41x + -10x = -51x
-51x + -3x + 30x2 = -12 + -6 + 54 + -108

Combine like terms: -51x + -3x = -54x
-54x + 30x2 = -12 + -6 + 54 + -108

Combine like terms: -12 + -6 = -18
-54x + 30x2 = -18 + 54 + -108

Combine like terms: -18 + 54 = 36
-54x + 30x2 = 36 + -108

Combine like terms: 36 + -108 = -72
-54x + 30x2 = -72

Solving
-54x + 30x2 = -72

Solving for variable 'x'.

Reorder the terms:
72 + -54x + 30x2 = -72 + 72

Combine like terms: -72 + 72 = 0
72 + -54x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + -9x + 5x2) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(12 + -9x + 5x2)' equal to zero and attempt to solve:

Simplifying
12 + -9x + 5x2 = 0

Solving
12 + -9x + 5x2 = 0

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
2.4 + -1.8x + x2 = 0

Move the constant term to the right:

Add '-2.4' to each side of the equation.
2.4 + -1.8x + -2.4 + x2 = 0 + -2.4

Reorder the terms:
2.4 + -2.4 + -1.8x + x2 = 0 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
0.0 + -1.8x + x2 = 0 + -2.4
-1.8x + x2 = 0 + -2.4

Combine like terms: 0 + -2.4 = -2.4
-1.8x + x2 = -2.4

The x term is -1.8x.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8x + 0.81 + x2 = -2.4 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = -2.4 + 0.81

Combine like terms: -2.4 + 0.81 = -1.59
0.81 + -1.8x + x2 = -1.59

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = -1.59

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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