(5x^2+49x-6)-(7x^2+5x-84)=12-2x

Solution for (5x^2+49x-6)-(7x^2+5x-84)=12-2x equation:

Simplifying
(5x2 + 49x + -6) + -1(7x2 + 5x + -84) = 12 + -2x

Reorder the terms:
(-6 + 49x + 5x2) + -1(7x2 + 5x + -84) = 12 + -2x

Remove parenthesis around (-6 + 49x + 5x2)
-6 + 49x + 5x2 + -1(7x2 + 5x + -84) = 12 + -2x

Reorder the terms:
-6 + 49x + 5x2 + -1(-84 + 5x + 7x2) = 12 + -2x
-6 + 49x + 5x2 + (-84 * -1 + 5x * -1 + 7x2 * -1) = 12 + -2x
-6 + 49x + 5x2 + (84 + -5x + -7x2) = 12 + -2x

Reorder the terms:
-6 + 84 + 49x + -5x + 5x2 + -7x2 = 12 + -2x

Combine like terms: -6 + 84 = 78
78 + 49x + -5x + 5x2 + -7x2 = 12 + -2x

Combine like terms: 49x + -5x = 44x
78 + 44x + 5x2 + -7x2 = 12 + -2x

Combine like terms: 5x2 + -7x2 = -2x2
78 + 44x + -2x2 = 12 + -2x

Solving
78 + 44x + -2x2 = 12 + -2x

Solving for variable 'x'.

Reorder the terms:
78 + -12 + 44x + 2x + -2x2 = 12 + -2x + -12 + 2x

Combine like terms: 78 + -12 = 66
66 + 44x + 2x + -2x2 = 12 + -2x + -12 + 2x

Combine like terms: 44x + 2x = 46x
66 + 46x + -2x2 = 12 + -2x + -12 + 2x

Reorder the terms:
66 + 46x + -2x2 = 12 + -12 + -2x + 2x

Combine like terms: 12 + -12 = 0
66 + 46x + -2x2 = 0 + -2x + 2x
66 + 46x + -2x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
66 + 46x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(33 + 23x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(33 + 23x + -1x2)' equal to zero and attempt to solve:

Simplifying
33 + 23x + -1x2 = 0

Solving
33 + 23x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-33 + -23x + x2 = 0

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -23x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + -23x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -23x + x2 = 0 + 33
-23x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
-23x + x2 = 33

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = 33 + 132.25

Reorder the terms:
132.25 + -23x + x2 = 33 + 132.25

Combine like terms: 33 + 132.25 = 165.25
132.25 + -23x + x2 = 165.25

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 165.25

Calculate the square root of the right side: 12.854960132

Break this problem into two subproblems by setting 
(x + -11.5) equal to 12.854960132 and -12.854960132.

Subproblem 1
x + -11.5 = 12.854960132

Simplifying
x + -11.5 = 12.854960132

Reorder the terms:
-11.5 + x = 12.854960132

Solving
-11.5 + x = 12.854960132

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = 12.854960132 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = 12.854960132 + 11.5
x = 12.854960132 + 11.5

Combine like terms: 12.854960132 + 11.5 = 24.354960132
x = 24.354960132

Simplifying
x = 24.354960132

Subproblem 2
x + -11.5 = -12.854960132

Simplifying
x + -11.5 = -12.854960132

Reorder the terms:
-11.5 + x = -12.854960132

Solving
-11.5 + x = -12.854960132

Solving for variable 'x'.

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

Add '11.5' to each side of the equation.
-11.5 + 11.5 + x = -12.854960132 + 11.5

Combine like terms: -11.5 + 11.5 = 0.0
0.0 + x = -12.854960132 + 11.5
x = -12.854960132 + 11.5

Combine like terms: -12.854960132 + 11.5 = -1.354960132
x = -1.354960132

Simplifying
x = -1.354960132

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {24.354960132, -1.354960132}
Solution
x = {24.354960132, -1.354960132}