3(x-1)-2(x^2+2x+3)-5(x+6)=0

Solution for 3(x-1)-2(x^2+2x+3)-5(x+6)=0 equation:

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

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

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

Reorder the terms:
-3 + 3x + -6 + -4x + -2x2 + -5(6 + x) = 0
-3 + 3x + -6 + -4x + -2x2 + (6 * -5 + x * -5) = 0
-3 + 3x + -6 + -4x + -2x2 + (-30 + -5x) = 0

Reorder the terms:
-3 + -6 + -30 + 3x + -4x + -5x + -2x2 = 0

Combine like terms: -3 + -6 = -9
-9 + -30 + 3x + -4x + -5x + -2x2 = 0

Combine like terms: -9 + -30 = -39
-39 + 3x + -4x + -5x + -2x2 = 0

Combine like terms: 3x + -4x = -1x
-39 + -1x + -5x + -2x2 = 0

Combine like terms: -1x + -5x = -6x
-39 + -6x + -2x2 = 0

Solving
-39 + -6x + -2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(39 + 6x + 2x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(39 + 6x + 2x2)' equal to zero and attempt to solve:

Simplifying
39 + 6x + 2x2 = 0

Solving
39 + 6x + 2x2 = 0

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

Divide each side by '2'.
19.5 + 3x + x2 = 0

Move the constant term to the right:

Add '-19.5' to each side of the equation.
19.5 + 3x + -19.5 + x2 = 0 + -19.5

Reorder the terms:
19.5 + -19.5 + 3x + x2 = 0 + -19.5

Combine like terms: 19.5 + -19.5 = 0.0
0.0 + 3x + x2 = 0 + -19.5
3x + x2 = 0 + -19.5

Combine like terms: 0 + -19.5 = -19.5
3x + x2 = -19.5

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -19.5 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -19.5 + 2.25

Combine like terms: -19.5 + 2.25 = -17.25
2.25 + 3x + x2 = -17.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = -17.25

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.