-1x=4x^2+5x-6

Solution for -1x=4x^2+5x-6 equation:

Simplifying
-1x = 4x2 + 5x + -6

Reorder the terms:
-1x = -6 + 5x + 4x2

Solving
-1x = -6 + 5x + 4x2

Solving for variable 'x'.

Reorder the terms:
6 + -1x + -5x + -4x2 = -6 + 5x + 4x2 + 6 + -5x + -4x2

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

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

Combine like terms: -6 + 6 = 0
6 + -6x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2
6 + -6x + -4x2 = 5x + -5x + 4x2 + -4x2

Combine like terms: 5x + -5x = 0
6 + -6x + -4x2 = 0 + 4x2 + -4x2
6 + -6x + -4x2 = 4x2 + -4x2

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

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

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

Simplifying
3 + -3x + -2x2 = 0

Solving
3 + -3x + -2x2 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 1.5x + x2 = 0 + 1.5
1.5x + x2 = 0 + 1.5

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

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 = 1.5 + 0.5625

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

Combine like terms: 1.5 + 0.5625 = 2.0625
0.5625 + 1.5x + x2 = 2.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 2.0625

Calculate the square root of the right side: 1.436140662

Break this problem into two subproblems by setting 
(x + 0.75) equal to 1.436140662 and -1.436140662.

Subproblem 1
x + 0.75 = 1.436140662

Simplifying
x + 0.75 = 1.436140662

Reorder the terms:
0.75 + x = 1.436140662

Solving
0.75 + x = 1.436140662

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 1.436140662 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 1.436140662 + -0.75
x = 1.436140662 + -0.75

Combine like terms: 1.436140662 + -0.75 = 0.686140662
x = 0.686140662

Simplifying
x = 0.686140662

Subproblem 2
x + 0.75 = -1.436140662

Simplifying
x + 0.75 = -1.436140662

Reorder the terms:
0.75 + x = -1.436140662

Solving
0.75 + x = -1.436140662

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -1.436140662 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -1.436140662 + -0.75
x = -1.436140662 + -0.75

Combine like terms: -1.436140662 + -0.75 = -2.186140662
x = -2.186140662

Simplifying
x = -2.186140662

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.686140662, -2.186140662}
Solution
x = {0.686140662, -2.186140662}