5(x+0.5)=-1.5x(x+3x)

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Solution for 5(x+0.5)=-1.5x(x+3x) equation: 


Simplifying
5(x + 0.5) = -1.5x(x + 3x)

Reorder the terms:
5(0.5 + x) = -1.5x(x + 3x)
(0.5 * 5 + x * 5) = -1.5x(x + 3x)
(2.5 + 5x) = -1.5x(x + 3x)

Combine like terms: x + 3x = 4x
2.5 + 5x = -1.5x(4x)

Remove parenthesis around (4x)
2.5 + 5x = -1.5x * 4x

Reorder the terms for easier multiplication:
2.5 + 5x = -1.5 * 4x * x

Multiply -1.5 * 4
2.5 + 5x = -6x * x

Multiply x * x
2.5 + 5x = -6x2

Solving
2.5 + 5x = -6x2

Solving for variable 'x'.

Combine like terms: -6x2 + 6x2 = 0
2.5 + 5x + 6x2 = 0

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

Divide each side by '6'.
0.4166666667 + 0.8333333333x + x2 = 0

Move the constant term to the right:

Add '-0.4166666667' to each side of the equation.
0.4166666667 + 0.8333333333x + -0.4166666667 + x2 = 0 + -0.4166666667

Reorder the terms:
0.4166666667 + -0.4166666667 + 0.8333333333x + x2 = 0 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + 0.8333333333x + x2 = 0 + -0.4166666667
0.8333333333x + x2 = 0 + -0.4166666667

Combine like terms: 0 + -0.4166666667 = -0.4166666667
0.8333333333x + x2 = -0.4166666667

The x term is 0.8333333333x.  Take half its coefficient (0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
0.8333333333x + 0.1736111111 + x2 = -0.4166666667 + 0.1736111111

Reorder the terms:
0.1736111111 + 0.8333333333x + x2 = -0.4166666667 + 0.1736111111

Combine like terms: -0.4166666667 + 0.1736111111 = -0.2430555556
0.1736111111 + 0.8333333333x + x2 = -0.2430555556

Factor a perfect square on the left side:
(x + 0.4166666667)(x + 0.4166666667) = -0.2430555556

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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