3x(2x-5)-6(2x^2-x+4)=

Solution for 3x(2x-5)-6(2x^2-x+4)= equation:

Simplifying
3x(2x + -5) + -6(2x2 + -1x + 4) = 0

Reorder the terms:
3x(-5 + 2x) + -6(2x2 + -1x + 4) = 0
(-5 * 3x + 2x * 3x) + -6(2x2 + -1x + 4) = 0
(-15x + 6x2) + -6(2x2 + -1x + 4) = 0

Reorder the terms:
-15x + 6x2 + -6(4 + -1x + 2x2) = 0
-15x + 6x2 + (4 * -6 + -1x * -6 + 2x2 * -6) = 0
-15x + 6x2 + (-24 + 6x + -12x2) = 0

Reorder the terms:
-24 + -15x + 6x + 6x2 + -12x2 = 0

Combine like terms: -15x + 6x = -9x
-24 + -9x + 6x2 + -12x2 = 0

Combine like terms: 6x2 + -12x2 = -6x2
-24 + -9x + -6x2 = 0

Solving
-24 + -9x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-3'.
-3(8 + 3x + 2x2) = 0

Ignore the factor -3.
Subproblem 1
Set the factor '(8 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
8 + 3x + 2x2 = 0

Solving
8 + 3x + 2x2 = 0

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

Divide each side by '2'.
4 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 1.5x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 1.5x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 1.5x + x2 = 0 + -4
1.5x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
1.5x + x2 = -4

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = -4 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -4 + 0.5625

Combine like terms: -4 + 0.5625 = -3.4375
0.5625 + 1.5x + x2 = -3.4375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = -3.4375

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.