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

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

Simplifying
(6x + 4)(-3 + x) + (2x + 6)(4 + -2x) = 0

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

Multiply (4 + 6x) * (-3 + x)
(4(-3 + x) + 6x * (-3 + x)) + (2x + 6)(4 + -2x) = 0
((-3 * 4 + x * 4) + 6x * (-3 + x)) + (2x + 6)(4 + -2x) = 0
((-12 + 4x) + 6x * (-3 + x)) + (2x + 6)(4 + -2x) = 0
(-12 + 4x + (-3 * 6x + x * 6x)) + (2x + 6)(4 + -2x) = 0
(-12 + 4x + (-18x + 6x2)) + (2x + 6)(4 + -2x) = 0

Combine like terms: 4x + -18x = -14x
(-12 + -14x + 6x2) + (2x + 6)(4 + -2x) = 0

Reorder the terms:
-12 + -14x + 6x2 + (6 + 2x)(4 + -2x) = 0

Multiply (6 + 2x) * (4 + -2x)
-12 + -14x + 6x2 + (6(4 + -2x) + 2x * (4 + -2x)) = 0
-12 + -14x + 6x2 + ((4 * 6 + -2x * 6) + 2x * (4 + -2x)) = 0
-12 + -14x + 6x2 + ((24 + -12x) + 2x * (4 + -2x)) = 0
-12 + -14x + 6x2 + (24 + -12x + (4 * 2x + -2x * 2x)) = 0
-12 + -14x + 6x2 + (24 + -12x + (8x + -4x2)) = 0

Combine like terms: -12x + 8x = -4x
-12 + -14x + 6x2 + (24 + -4x + -4x2) = 0

Reorder the terms:
-12 + 24 + -14x + -4x + 6x2 + -4x2 = 0

Combine like terms: -12 + 24 = 12
12 + -14x + -4x + 6x2 + -4x2 = 0

Combine like terms: -14x + -4x = -18x
12 + -18x + 6x2 + -4x2 = 0

Combine like terms: 6x2 + -4x2 = 2x2
12 + -18x + 2x2 = 0

Solving
12 + -18x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + -9x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
6 + -9x + x2 = 0

Solving
6 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + -9x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + -9x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -9x + x2 = 0 + -6
-9x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
-9x + x2 = -6

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = -6 + 20.25

Reorder the terms:
20.25 + -9x + x2 = -6 + 20.25

Combine like terms: -6 + 20.25 = 14.25
20.25 + -9x + x2 = 14.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(x + -4.5) equal to 3.774917218 and -3.774917218.

Subproblem 1
x + -4.5 = 3.774917218

Simplifying
x + -4.5 = 3.774917218

Reorder the terms:
-4.5 + x = 3.774917218

Solving
-4.5 + x = 3.774917218

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 3.774917218 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 3.774917218 + 4.5
x = 3.774917218 + 4.5

Combine like terms: 3.774917218 + 4.5 = 8.274917218
x = 8.274917218

Simplifying
x = 8.274917218

Subproblem 2
x + -4.5 = -3.774917218

Simplifying
x + -4.5 = -3.774917218

Reorder the terms:
-4.5 + x = -3.774917218

Solving
-4.5 + x = -3.774917218

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -3.774917218 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -3.774917218 + 4.5
x = -3.774917218 + 4.5

Combine like terms: -3.774917218 + 4.5 = 0.725082782
x = 0.725082782

Simplifying
x = 0.725082782

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.274917218, 0.725082782}
Solution
x = {8.274917218, 0.725082782}