5x(3x+1)=2(2x-3)

Solution for 5x(3x+1)=2(2x-3) equation:

Simplifying
5x(3x + 1) = 2(2x + -3)

Reorder the terms:
5x(1 + 3x) = 2(2x + -3)
(1 * 5x + 3x * 5x) = 2(2x + -3)
(5x + 15x2) = 2(2x + -3)

Reorder the terms:
5x + 15x2 = 2(-3 + 2x)
5x + 15x2 = (-3 * 2 + 2x * 2)
5x + 15x2 = (-6 + 4x)

Solving
5x + 15x2 = -6 + 4x

Solving for variable 'x'.

Reorder the terms:
6 + 5x + -4x + 15x2 = -6 + 4x + 6 + -4x

Combine like terms: 5x + -4x = 1x
6 + 1x + 15x2 = -6 + 4x + 6 + -4x

Reorder the terms:
6 + 1x + 15x2 = -6 + 6 + 4x + -4x

Combine like terms: -6 + 6 = 0
6 + 1x + 15x2 = 0 + 4x + -4x
6 + 1x + 15x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
6 + 1x + 15x2 = 0

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

Divide each side by '15'.
0.4 + 0.06666666667x + x2 = 0

Move the constant term to the right:

Add '-0.4' to each side of the equation.
0.4 + 0.06666666667x + -0.4 + x2 = 0 + -0.4

Reorder the terms:
0.4 + -0.4 + 0.06666666667x + x2 = 0 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + 0.06666666667x + x2 = 0 + -0.4
0.06666666667x + x2 = 0 + -0.4

Combine like terms: 0 + -0.4 = -0.4
0.06666666667x + x2 = -0.4

The x term is 0.06666666667x.  Take half its coefficient (0.03333333334).
Square it (0.001111111112) and add it to both sides.

Add '0.001111111112' to each side of the equation.
0.06666666667x + 0.001111111112 + x2 = -0.4 + 0.001111111112

Reorder the terms:
0.001111111112 + 0.06666666667x + x2 = -0.4 + 0.001111111112

Combine like terms: -0.4 + 0.001111111112 = -0.398888888888
0.001111111112 + 0.06666666667x + x2 = -0.398888888888

Factor a perfect square on the left side:
(x + 0.03333333334)(x + 0.03333333334) = -0.398888888888

Can't calculate square root of the right side.

The solution to this equation could not be determined.