15x^2-27x-6=-48

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Solution for 15x^2-27x-6=-48 equation: 


Simplifying
15x2 + -27x + -6 = -48

Reorder the terms:
-6 + -27x + 15x2 = -48

Solving
-6 + -27x + 15x2 = -48

Solving for variable 'x'.

Reorder the terms:
-6 + 48 + -27x + 15x2 = -48 + 48

Combine like terms: -6 + 48 = 42
42 + -27x + 15x2 = -48 + 48

Combine like terms: -48 + 48 = 0
42 + -27x + 15x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(14 + -9x + 5x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(14 + -9x + 5x2)' equal to zero and attempt to solve:

Simplifying
14 + -9x + 5x2 = 0

Solving
14 + -9x + 5x2 = 0

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

Divide each side by '5'.
2.8 + -1.8x + x2 = 0

Move the constant term to the right:

Add '-2.8' to each side of the equation.
2.8 + -1.8x + -2.8 + x2 = 0 + -2.8

Reorder the terms:
2.8 + -2.8 + -1.8x + x2 = 0 + -2.8

Combine like terms: 2.8 + -2.8 = 0.0
0.0 + -1.8x + x2 = 0 + -2.8
-1.8x + x2 = 0 + -2.8

Combine like terms: 0 + -2.8 = -2.8
-1.8x + x2 = -2.8

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 = -2.8 + 0.81

Reorder the terms:
0.81 + -1.8x + x2 = -2.8 + 0.81

Combine like terms: -2.8 + 0.81 = -1.99
0.81 + -1.8x + x2 = -1.99

Factor a perfect square on the left side:
(x + -0.9)(x + -0.9) = -1.99

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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