-5x(2x-1)=3(x+4)

Solution for -5x(2x-1)=3(x+4) equation:

Simplifying
-5x(2x + -1) = 3(x + 4)

Reorder the terms:
-5x(-1 + 2x) = 3(x + 4)
(-1 * -5x + 2x * -5x) = 3(x + 4)
(5x + -10x2) = 3(x + 4)

Reorder the terms:
5x + -10x2 = 3(4 + x)
5x + -10x2 = (4 * 3 + x * 3)
5x + -10x2 = (12 + 3x)

Solving
5x + -10x2 = 12 + 3x

Solving for variable 'x'.

Reorder the terms:
-12 + 5x + -3x + -10x2 = 12 + 3x + -12 + -3x

Combine like terms: 5x + -3x = 2x
-12 + 2x + -10x2 = 12 + 3x + -12 + -3x

Reorder the terms:
-12 + 2x + -10x2 = 12 + -12 + 3x + -3x

Combine like terms: 12 + -12 = 0
-12 + 2x + -10x2 = 0 + 3x + -3x
-12 + 2x + -10x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-12 + 2x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + x + -5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + x + -5x2)' equal to zero and attempt to solve:

Simplifying
-6 + x + -5x2 = 0

Solving
-6 + x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
1.2 + -0.2x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + -0.2x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + -0.2x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + -0.2x + x2 = 0 + -1.2
-0.2x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
-0.2x + x2 = -1.2

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-0.2x + 0.25 + x2 = -1.2 + 0.25

Reorder the terms:
0.25 + -0.2x + x2 = -1.2 + 0.25

Combine like terms: -1.2 + 0.25 = -0.95
0.25 + -0.2x + x2 = -0.95

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -0.95

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.