9x(2x+5)=-3x-75

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Solution for 9x(2x+5)=-3x-75 equation: 


Simplifying
9x(2x + 5) = -3x + -75

Reorder the terms:
9x(5 + 2x) = -3x + -75
(5 * 9x + 2x * 9x) = -3x + -75
(45x + 18x2) = -3x + -75

Reorder the terms:
45x + 18x2 = -75 + -3x

Solving
45x + 18x2 = -75 + -3x

Solving for variable 'x'.

Reorder the terms:
75 + 45x + 3x + 18x2 = -75 + -3x + 75 + 3x

Combine like terms: 45x + 3x = 48x
75 + 48x + 18x2 = -75 + -3x + 75 + 3x

Reorder the terms:
75 + 48x + 18x2 = -75 + 75 + -3x + 3x

Combine like terms: -75 + 75 = 0
75 + 48x + 18x2 = 0 + -3x + 3x
75 + 48x + 18x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
75 + 48x + 18x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(25 + 16x + 6x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(25 + 16x + 6x2)' equal to zero and attempt to solve:

Simplifying
25 + 16x + 6x2 = 0

Solving
25 + 16x + 6x2 = 0

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

Divide each side by '6'.
4.166666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-4.166666667' to each side of the equation.
4.166666667 + 2.666666667x + -4.166666667 + x2 = 0 + -4.166666667

Reorder the terms:
4.166666667 + -4.166666667 + 2.666666667x + x2 = 0 + -4.166666667

Combine like terms: 4.166666667 + -4.166666667 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + -4.166666667
2.666666667x + x2 = 0 + -4.166666667

Combine like terms: 0 + -4.166666667 = -4.166666667
2.666666667x + x2 = -4.166666667

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 = -4.166666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -4.166666667 + 1.777777780

Combine like terms: -4.166666667 + 1.777777780 = -2.388888887
1.777777780 + 2.666666667x + x2 = -2.388888887

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = -2.388888887

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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