3x(-3x-9)=111

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Solution for 3x(-3x-9)=111 equation: 


Simplifying
3x(-3x + -9) = 111

Reorder the terms:
3x(-9 + -3x) = 111
(-9 * 3x + -3x * 3x) = 111
(-27x + -9x2) = 111

Solving
-27x + -9x2 = 111

Solving for variable 'x'.

Reorder the terms:
-111 + -27x + -9x2 = 111 + -111

Combine like terms: 111 + -111 = 0
-111 + -27x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(37 + 9x + 3x2) = 0

Ignore the factor -3.

Subproblem 1
Set the factor '(37 + 9x + 3x2)' equal to zero and attempt to solve:

Simplifying
37 + 9x + 3x2 = 0

Solving
37 + 9x + 3x2 = 0

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

Divide each side by '3'.
12.33333333 + 3x + x2 = 0

Move the constant term to the right:

Add '-12.33333333' to each side of the equation.
12.33333333 + 3x + -12.33333333 + x2 = 0 + -12.33333333

Reorder the terms:
12.33333333 + -12.33333333 + 3x + x2 = 0 + -12.33333333

Combine like terms: 12.33333333 + -12.33333333 = 0.00000000
0.00000000 + 3x + x2 = 0 + -12.33333333
3x + x2 = 0 + -12.33333333

Combine like terms: 0 + -12.33333333 = -12.33333333
3x + x2 = -12.33333333

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 = -12.33333333 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -12.33333333 + 2.25

Combine like terms: -12.33333333 + 2.25 = -10.08333333
2.25 + 3x + x2 = -10.08333333

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -10.08333333

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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