-3x(x+4)-4x=24

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Solution for -3x(x+4)-4x=24 equation: 


Simplifying
-3x(x + 4) + -4x = 24

Reorder the terms:
-3x(4 + x) + -4x = 24
(4 * -3x + x * -3x) + -4x = 24
(-12x + -3x2) + -4x = 24

Reorder the terms:
-12x + -4x + -3x2 = 24

Combine like terms: -12x + -4x = -16x
-16x + -3x2 = 24

Solving
-16x + -3x2 = 24

Solving for variable 'x'.

Reorder the terms:
-24 + -16x + -3x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + -16x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(24 + 16x + 3x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(24 + 16x + 3x2)' equal to zero and attempt to solve:

Simplifying
24 + 16x + 3x2 = 0

Solving
24 + 16x + 3x2 = 0

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

Divide each side by '3'.
8 + 5.333333333x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 5.333333333x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 5.333333333x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5.333333333x + x2 = 0 + -8
5.333333333x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
5.333333333x + x2 = -8

The x term is 5.333333333x.  Take half its coefficient (2.666666667).
Square it (7.111111113) and add it to both sides.

Add '7.111111113' to each side of the equation.
5.333333333x + 7.111111113 + x2 = -8 + 7.111111113

Reorder the terms:
7.111111113 + 5.333333333x + x2 = -8 + 7.111111113

Combine like terms: -8 + 7.111111113 = -0.888888887
7.111111113 + 5.333333333x + x2 = -0.888888887

Factor a perfect square on the left side:
(x + 2.666666667)(x + 2.666666667) = -0.888888887

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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