5x(-3x+8)=115

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Solution for 5x(-3x+8)=115 equation: 


Simplifying
5x(-3x + 8) = 115

Reorder the terms:
5x(8 + -3x) = 115
(8 * 5x + -3x * 5x) = 115
(40x + -15x2) = 115

Solving
40x + -15x2 = 115

Solving for variable 'x'.

Reorder the terms:
-115 + 40x + -15x2 = 115 + -115

Combine like terms: 115 + -115 = 0
-115 + 40x + -15x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-23 + 8x + -3x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-23 + 8x + -3x2)' equal to zero and attempt to solve:

Simplifying
-23 + 8x + -3x2 = 0

Solving
-23 + 8x + -3x2 = 0

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

Divide each side by '-3'.
7.666666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '-7.666666667' to each side of the equation.
7.666666667 + -2.666666667x + -7.666666667 + x2 = 0 + -7.666666667

Reorder the terms:
7.666666667 + -7.666666667 + -2.666666667x + x2 = 0 + -7.666666667

Combine like terms: 7.666666667 + -7.666666667 = 0.000000000
0.000000000 + -2.666666667x + x2 = 0 + -7.666666667
-2.666666667x + x2 = 0 + -7.666666667

Combine like terms: 0 + -7.666666667 = -7.666666667
-2.666666667x + x2 = -7.666666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = -7.666666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = -7.666666667 + 1.777777780

Combine like terms: -7.666666667 + 1.777777780 = -5.888888887
1.777777780 + -2.666666667x + x2 = -5.888888887

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = -5.888888887

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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