-3x(3+x)+4(x-6)=-4

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Solution for -3x(3+x)+4(x-6)=-4 equation:


Simplifying
-3x(3 + x) + 4(x + -6) = -4
(3 * -3x + x * -3x) + 4(x + -6) = -4
(-9x + -3x2) + 4(x + -6) = -4

Reorder the terms:
-9x + -3x2 + 4(-6 + x) = -4
-9x + -3x2 + (-6 * 4 + x * 4) = -4
-9x + -3x2 + (-24 + 4x) = -4

Reorder the terms:
-24 + -9x + 4x + -3x2 = -4

Combine like terms: -9x + 4x = -5x
-24 + -5x + -3x2 = -4

Solving
-24 + -5x + -3x2 = -4

Solving for variable 'x'.

Reorder the terms:
-24 + 4 + -5x + -3x2 = -4 + 4

Combine like terms: -24 + 4 = -20
-20 + -5x + -3x2 = -4 + 4

Combine like terms: -4 + 4 = 0
-20 + -5x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(20 + 5x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(20 + 5x + 3x2)' equal to zero and attempt to solve:

Simplifying
20 + 5x + 3x2 = 0

Solving
20 + 5x + 3x2 = 0

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

Divide each side by '3'.
6.666666667 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + 1.666666667x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + 1.666666667x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + 1.666666667x + x2 = 0 + -6.666666667
1.666666667x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
1.666666667x + x2 = -6.666666667

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = -6.666666667 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = -6.666666667 + 0.6944444447

Combine like terms: -6.666666667 + 0.6944444447 = -5.9722222223
0.6944444447 + 1.666666667x + x2 = -5.9722222223

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = -5.9722222223

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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