3x*-2(x+6)=4x-(x-10)

Solution for 3x*-2(x+6)=4x-(x-10) equation:

Simplifying
3x * -2(x + 6) = 4x + -1(x + -10)

Reorder the terms:
3x * -2(6 + x) = 4x + -1(x + -10)

Reorder the terms for easier multiplication:
3 * -2x(6 + x) = 4x + -1(x + -10)

Multiply 3 * -2
-6x(6 + x) = 4x + -1(x + -10)
(6 * -6x + x * -6x) = 4x + -1(x + -10)
(-36x + -6x2) = 4x + -1(x + -10)

Reorder the terms:
-36x + -6x2 = 4x + -1(-10 + x)
-36x + -6x2 = 4x + (-10 * -1 + x * -1)
-36x + -6x2 = 4x + (10 + -1x)

Reorder the terms:
-36x + -6x2 = 10 + 4x + -1x

Combine like terms: 4x + -1x = 3x
-36x + -6x2 = 10 + 3x

Solving
-36x + -6x2 = 10 + 3x

Solving for variable 'x'.

Reorder the terms:
-10 + -36x + -3x + -6x2 = 10 + 3x + -10 + -3x

Combine like terms: -36x + -3x = -39x
-10 + -39x + -6x2 = 10 + 3x + -10 + -3x

Reorder the terms:
-10 + -39x + -6x2 = 10 + -10 + 3x + -3x

Combine like terms: 10 + -10 = 0
-10 + -39x + -6x2 = 0 + 3x + -3x
-10 + -39x + -6x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-10 + -39x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 39x + 6x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(10 + 39x + 6x2)' equal to zero and attempt to solve:

Simplifying
10 + 39x + 6x2 = 0

Solving
10 + 39x + 6x2 = 0

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

Divide each side by '6'.
1.666666667 + 6.5x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 6.5x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 6.5x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 6.5x + x2 = 0 + -1.666666667
6.5x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
6.5x + x2 = -1.666666667

The x term is 6.5x.  Take half its coefficient (3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
6.5x + 10.5625 + x2 = -1.666666667 + 10.5625

Reorder the terms:
10.5625 + 6.5x + x2 = -1.666666667 + 10.5625

Combine like terms: -1.666666667 + 10.5625 = 8.895833333
10.5625 + 6.5x + x2 = 8.895833333

Factor a perfect square on the left side:
(x + 3.25)(x + 3.25) = 8.895833333

Calculate the square root of the right side: 2.982588361

Break this problem into two subproblems by setting 
(x + 3.25) equal to 2.982588361 and -2.982588361.

Subproblem 1
x + 3.25 = 2.982588361

Simplifying
x + 3.25 = 2.982588361

Reorder the terms:
3.25 + x = 2.982588361

Solving
3.25 + x = 2.982588361

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = 2.982588361 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = 2.982588361 + -3.25
x = 2.982588361 + -3.25

Combine like terms: 2.982588361 + -3.25 = -0.267411639
x = -0.267411639

Simplifying
x = -0.267411639

Subproblem 2
x + 3.25 = -2.982588361

Simplifying
x + 3.25 = -2.982588361

Reorder the terms:
3.25 + x = -2.982588361

Solving
3.25 + x = -2.982588361

Solving for variable 'x'.

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

Add '-3.25' to each side of the equation.
3.25 + -3.25 + x = -2.982588361 + -3.25

Combine like terms: 3.25 + -3.25 = 0.00
0.00 + x = -2.982588361 + -3.25
x = -2.982588361 + -3.25

Combine like terms: -2.982588361 + -3.25 = -6.232588361
x = -6.232588361

Simplifying
x = -6.232588361

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.267411639, -6.232588361}
Solution
x = {-0.267411639, -6.232588361}