0=3(6x^2)-4(-11x)+5(-10)

Solution for 0=3(6x^2)-4(-11x)+5(-10) equation:

Simplifying
0 = 3(6x2) + -4(-11x) + 5(-10)

Remove parenthesis around (6x2)
0 = 3 * 6x2 + -4(-11x) + 5(-10)

Multiply 3 * 6
0 = 18x2 + -4(-11x) + 5(-10)

Remove parenthesis around (-11x)
0 = 18x2 + -4 * -11x + 5(-10)

Multiply -4 * -11
0 = 18x2 + 44x + 5(-10)

Multiply 5 * -10
0 = 18x2 + 44x + -50

Reorder the terms:
0 = -50 + 44x + 18x2

Solving
0 = -50 + 44x + 18x2

Solving for variable 'x'.

Combine like terms: 0 + 50 = 50
50 + -44x + -18x2 = -50 + 44x + 18x2 + 50 + -44x + -18x2

Reorder the terms:
50 + -44x + -18x2 = -50 + 50 + 44x + -44x + 18x2 + -18x2

Combine like terms: -50 + 50 = 0
50 + -44x + -18x2 = 0 + 44x + -44x + 18x2 + -18x2
50 + -44x + -18x2 = 44x + -44x + 18x2 + -18x2

Combine like terms: 44x + -44x = 0
50 + -44x + -18x2 = 0 + 18x2 + -18x2
50 + -44x + -18x2 = 18x2 + -18x2

Combine like terms: 18x2 + -18x2 = 0
50 + -44x + -18x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -22x + -9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(25 + -22x + -9x2)' equal to zero and attempt to solve:

Simplifying
25 + -22x + -9x2 = 0

Solving
25 + -22x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-2.777777778 + 2.444444444x + x2 = 0

Move the constant term to the right:

Add '2.777777778' to each side of the equation.
-2.777777778 + 2.444444444x + 2.777777778 + x2 = 0 + 2.777777778

Reorder the terms:
-2.777777778 + 2.777777778 + 2.444444444x + x2 = 0 + 2.777777778

Combine like terms: -2.777777778 + 2.777777778 = 0.000000000
0.000000000 + 2.444444444x + x2 = 0 + 2.777777778
2.444444444x + x2 = 0 + 2.777777778

Combine like terms: 0 + 2.777777778 = 2.777777778
2.444444444x + x2 = 2.777777778

The x term is 2.444444444x.  Take half its coefficient (1.222222222).
Square it (1.493827160) and add it to both sides.

Add '1.493827160' to each side of the equation.
2.444444444x + 1.493827160 + x2 = 2.777777778 + 1.493827160

Reorder the terms:
1.493827160 + 2.444444444x + x2 = 2.777777778 + 1.493827160

Combine like terms: 2.777777778 + 1.493827160 = 4.271604938
1.493827160 + 2.444444444x + x2 = 4.271604938

Factor a perfect square on the left side:
(x + 1.222222222)(x + 1.222222222) = 4.271604938

Calculate the square root of the right side: 2.066786137

Break this problem into two subproblems by setting 
(x + 1.222222222) equal to 2.066786137 and -2.066786137.

Subproblem 1
x + 1.222222222 = 2.066786137

Simplifying
x + 1.222222222 = 2.066786137

Reorder the terms:
1.222222222 + x = 2.066786137

Solving
1.222222222 + x = 2.066786137

Solving for variable 'x'.

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

Add '-1.222222222' to each side of the equation.
1.222222222 + -1.222222222 + x = 2.066786137 + -1.222222222

Combine like terms: 1.222222222 + -1.222222222 = 0.000000000
0.000000000 + x = 2.066786137 + -1.222222222
x = 2.066786137 + -1.222222222

Combine like terms: 2.066786137 + -1.222222222 = 0.844563915
x = 0.844563915

Simplifying
x = 0.844563915

Subproblem 2
x + 1.222222222 = -2.066786137

Simplifying
x + 1.222222222 = -2.066786137

Reorder the terms:
1.222222222 + x = -2.066786137

Solving
1.222222222 + x = -2.066786137

Solving for variable 'x'.

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

Add '-1.222222222' to each side of the equation.
1.222222222 + -1.222222222 + x = -2.066786137 + -1.222222222

Combine like terms: 1.222222222 + -1.222222222 = 0.000000000
0.000000000 + x = -2.066786137 + -1.222222222
x = -2.066786137 + -1.222222222

Combine like terms: -2.066786137 + -1.222222222 = -3.289008359
x = -3.289008359

Simplifying
x = -3.289008359

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.844563915, -3.289008359}
Solution
x = {0.844563915, -3.289008359}