-3x(3x-2)=-3x+24

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Solution for -3x(3x-2)=-3x+24 equation: 


Simplifying
-3x(3x + -2) = -3x + 24

Reorder the terms:
-3x(-2 + 3x) = -3x + 24
(-2 * -3x + 3x * -3x) = -3x + 24
(6x + -9x2) = -3x + 24

Reorder the terms:
6x + -9x2 = 24 + -3x

Solving
6x + -9x2 = 24 + -3x

Solving for variable 'x'.

Reorder the terms:
-24 + 6x + 3x + -9x2 = 24 + -3x + -24 + 3x

Combine like terms: 6x + 3x = 9x
-24 + 9x + -9x2 = 24 + -3x + -24 + 3x

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

Combine like terms: 24 + -24 = 0
-24 + 9x + -9x2 = 0 + -3x + 3x
-24 + 9x + -9x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-24 + 9x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-8 + 3x + -3x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-8 + 3x + -3x2)' equal to zero and attempt to solve:

Simplifying
-8 + 3x + -3x2 = 0

Solving
-8 + 3x + -3x2 = 0

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

Divide each side by '-3'.
2.666666667 + -1x + x2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + -1x + -2.666666667 + x2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + -1x + x2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + -1x + x2 = 0 + -2.666666667
-1x + x2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
-1x + x2 = -2.666666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -2.666666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -2.666666667 + 0.25

Combine like terms: -2.666666667 + 0.25 = -2.416666667
0.25 + -1x + x2 = -2.416666667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -2.416666667

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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