15x-30-6x-3x^2=0

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Solution for 15x-30-6x-3x^2=0 equation: 


Simplifying
15x + -30 + -6x + -3x2 = 0

Reorder the terms:
-30 + 15x + -6x + -3x2 = 0

Combine like terms: 15x + -6x = 9x
-30 + 9x + -3x2 = 0

Solving
-30 + 9x + -3x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-10 + 3x + -1x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-10 + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
-10 + 3x + -1x2 = 0

Solving
-10 + 3x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
10 + -3x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + -3x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + -3x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -3x + x2 = 0 + -10
-3x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
-3x + x2 = -10

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -10 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -10 + 2.25

Combine like terms: -10 + 2.25 = -7.75
2.25 + -3x + x2 = -7.75

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = -7.75

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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