2x(-4x+23)=108

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Solution for 2x(-4x+23)=108 equation: 


Simplifying
2x(-4x + 23) = 108

Reorder the terms:
2x(23 + -4x) = 108
(23 * 2x + -4x * 2x) = 108
(46x + -8x2) = 108

Solving
46x + -8x2 = 108

Solving for variable 'x'.

Reorder the terms:
-108 + 46x + -8x2 = 108 + -108

Combine like terms: 108 + -108 = 0
-108 + 46x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-54 + 23x + -4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-54 + 23x + -4x2)' equal to zero and attempt to solve:

Simplifying
-54 + 23x + -4x2 = 0

Solving
-54 + 23x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
13.5 + -5.75x + x2 = 0

Move the constant term to the right:

Add '-13.5' to each side of the equation.
13.5 + -5.75x + -13.5 + x2 = 0 + -13.5

Reorder the terms:
13.5 + -13.5 + -5.75x + x2 = 0 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + -5.75x + x2 = 0 + -13.5
-5.75x + x2 = 0 + -13.5

Combine like terms: 0 + -13.5 = -13.5
-5.75x + x2 = -13.5

The x term is -5.75x.  Take half its coefficient (-2.875).
Square it (8.265625) and add it to both sides.

Add '8.265625' to each side of the equation.
-5.75x + 8.265625 + x2 = -13.5 + 8.265625

Reorder the terms:
8.265625 + -5.75x + x2 = -13.5 + 8.265625

Combine like terms: -13.5 + 8.265625 = -5.234375
8.265625 + -5.75x + x2 = -5.234375

Factor a perfect square on the left side:
(x + -2.875)(x + -2.875) = -5.234375

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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