6(3x^2-4x^2+11x-5)-10(-2x^2-6x^2+6x+7)=

Solution for 6(3x^2-4x^2+11x-5)-10(-2x^2-6x^2+6x+7)= equation:

Simplifying
6(3x2 + -4x2 + 11x + -5) + -10(-2x2 + -6x2 + 6x + 7) = 0

Reorder the terms:
6(-5 + 11x + 3x2 + -4x2) + -10(-2x2 + -6x2 + 6x + 7) = 0

Combine like terms: 3x2 + -4x2 = -1x2
6(-5 + 11x + -1x2) + -10(-2x2 + -6x2 + 6x + 7) = 0
(-5 * 6 + 11x * 6 + -1x2 * 6) + -10(-2x2 + -6x2 + 6x + 7) = 0
(-30 + 66x + -6x2) + -10(-2x2 + -6x2 + 6x + 7) = 0

Reorder the terms:
-30 + 66x + -6x2 + -10(7 + 6x + -2x2 + -6x2) = 0

Combine like terms: -2x2 + -6x2 = -8x2
-30 + 66x + -6x2 + -10(7 + 6x + -8x2) = 0
-30 + 66x + -6x2 + (7 * -10 + 6x * -10 + -8x2 * -10) = 0
-30 + 66x + -6x2 + (-70 + -60x + 80x2) = 0

Reorder the terms:
-30 + -70 + 66x + -60x + -6x2 + 80x2 = 0

Combine like terms: -30 + -70 = -100
-100 + 66x + -60x + -6x2 + 80x2 = 0

Combine like terms: 66x + -60x = 6x
-100 + 6x + -6x2 + 80x2 = 0

Combine like terms: -6x2 + 80x2 = 74x2
-100 + 6x + 74x2 = 0

Solving
-100 + 6x + 74x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-50 + 3x + 37x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-50 + 3x + 37x2)' equal to zero and attempt to solve:

Simplifying
-50 + 3x + 37x2 = 0

Solving
-50 + 3x + 37x2 = 0

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

Divide each side by '37'.
-1.351351351 + 0.08108108108x + x2 = 0

Move the constant term to the right:

Add '1.351351351' to each side of the equation.
-1.351351351 + 0.08108108108x + 1.351351351 + x2 = 0 + 1.351351351

Reorder the terms:
-1.351351351 + 1.351351351 + 0.08108108108x + x2 = 0 + 1.351351351

Combine like terms: -1.351351351 + 1.351351351 = 0.000000000
0.000000000 + 0.08108108108x + x2 = 0 + 1.351351351
0.08108108108x + x2 = 0 + 1.351351351

Combine like terms: 0 + 1.351351351 = 1.351351351
0.08108108108x + x2 = 1.351351351

The x term is 0.08108108108x.  Take half its coefficient (0.04054054054).
Square it (0.001643535427) and add it to both sides.

Add '0.001643535427' to each side of the equation.
0.08108108108x + 0.001643535427 + x2 = 1.351351351 + 0.001643535427

Reorder the terms:
0.001643535427 + 0.08108108108x + x2 = 1.351351351 + 0.001643535427

Combine like terms: 1.351351351 + 0.001643535427 = 1.352994886427
0.001643535427 + 0.08108108108x + x2 = 1.352994886427

Factor a perfect square on the left side:
(x + 0.04054054054)(x + 0.04054054054) = 1.352994886427

Calculate the square root of the right side: 1.163183084

Break this problem into two subproblems by setting 
(x + 0.04054054054) equal to 1.163183084 and -1.163183084.

Subproblem 1
x + 0.04054054054 = 1.163183084

Simplifying
x + 0.04054054054 = 1.163183084

Reorder the terms:
0.04054054054 + x = 1.163183084

Solving
0.04054054054 + x = 1.163183084

Solving for variable 'x'.

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

Add '-0.04054054054' to each side of the equation.
0.04054054054 + -0.04054054054 + x = 1.163183084 + -0.04054054054

Combine like terms: 0.04054054054 + -0.04054054054 = 0.00000000000
0.00000000000 + x = 1.163183084 + -0.04054054054
x = 1.163183084 + -0.04054054054

Combine like terms: 1.163183084 + -0.04054054054 = 1.12264254346
x = 1.12264254346

Simplifying
x = 1.12264254346

Subproblem 2
x + 0.04054054054 = -1.163183084

Simplifying
x + 0.04054054054 = -1.163183084

Reorder the terms:
0.04054054054 + x = -1.163183084

Solving
0.04054054054 + x = -1.163183084

Solving for variable 'x'.

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

Add '-0.04054054054' to each side of the equation.
0.04054054054 + -0.04054054054 + x = -1.163183084 + -0.04054054054

Combine like terms: 0.04054054054 + -0.04054054054 = 0.00000000000
0.00000000000 + x = -1.163183084 + -0.04054054054
x = -1.163183084 + -0.04054054054

Combine like terms: -1.163183084 + -0.04054054054 = -1.20372362454
x = -1.20372362454

Simplifying
x = -1.20372362454

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.12264254346, -1.20372362454}
Solution
x = {1.12264254346, -1.20372362454}