(7-3x)x(-10)=22-2(4-x)

Solution for (7-3x)x(-10)=22-2(4-x) equation:

Simplifying
(7 + -3x) * x(-10) = 22 + -2(4 + -1x)

Reorder the terms for easier multiplication:
-10x(7 + -3x) = 22 + -2(4 + -1x)
(7 * -10x + -3x * -10x) = 22 + -2(4 + -1x)
(-70x + 30x2) = 22 + -2(4 + -1x)
-70x + 30x2 = 22 + (4 * -2 + -1x * -2)
-70x + 30x2 = 22 + (-8 + 2x)

Combine like terms: 22 + -8 = 14
-70x + 30x2 = 14 + 2x

Solving
-70x + 30x2 = 14 + 2x

Solving for variable 'x'.

Reorder the terms:
-14 + -70x + -2x + 30x2 = 14 + 2x + -14 + -2x

Combine like terms: -70x + -2x = -72x
-14 + -72x + 30x2 = 14 + 2x + -14 + -2x

Reorder the terms:
-14 + -72x + 30x2 = 14 + -14 + 2x + -2x

Combine like terms: 14 + -14 = 0
-14 + -72x + 30x2 = 0 + 2x + -2x
-14 + -72x + 30x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-14 + -72x + 30x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -36x + 15x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -36x + 15x2)' equal to zero and attempt to solve:

Simplifying
-7 + -36x + 15x2 = 0

Solving
-7 + -36x + 15x2 = 0

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

Divide each side by '15'.
-0.4666666667 + -2.4x + x2 = 0

Move the constant term to the right:

Add '0.4666666667' to each side of the equation.
-0.4666666667 + -2.4x + 0.4666666667 + x2 = 0 + 0.4666666667

Reorder the terms:
-0.4666666667 + 0.4666666667 + -2.4x + x2 = 0 + 0.4666666667

Combine like terms: -0.4666666667 + 0.4666666667 = 0.0000000000
0.0000000000 + -2.4x + x2 = 0 + 0.4666666667
-2.4x + x2 = 0 + 0.4666666667

Combine like terms: 0 + 0.4666666667 = 0.4666666667
-2.4x + x2 = 0.4666666667

The x term is -2.4x.  Take half its coefficient (-1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
-2.4x + 1.44 + x2 = 0.4666666667 + 1.44

Reorder the terms:
1.44 + -2.4x + x2 = 0.4666666667 + 1.44

Combine like terms: 0.4666666667 + 1.44 = 1.9066666667
1.44 + -2.4x + x2 = 1.9066666667

Factor a perfect square on the left side:
(x + -1.2)(x + -1.2) = 1.9066666667

Calculate the square root of the right side: 1.380821012

Break this problem into two subproblems by setting 
(x + -1.2) equal to 1.380821012 and -1.380821012.

Subproblem 1
x + -1.2 = 1.380821012

Simplifying
x + -1.2 = 1.380821012

Reorder the terms:
-1.2 + x = 1.380821012

Solving
-1.2 + x = 1.380821012

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = 1.380821012 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = 1.380821012 + 1.2
x = 1.380821012 + 1.2

Combine like terms: 1.380821012 + 1.2 = 2.580821012
x = 2.580821012

Simplifying
x = 2.580821012

Subproblem 2
x + -1.2 = -1.380821012

Simplifying
x + -1.2 = -1.380821012

Reorder the terms:
-1.2 + x = -1.380821012

Solving
-1.2 + x = -1.380821012

Solving for variable 'x'.

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

Add '1.2' to each side of the equation.
-1.2 + 1.2 + x = -1.380821012 + 1.2

Combine like terms: -1.2 + 1.2 = 0.0
0.0 + x = -1.380821012 + 1.2
x = -1.380821012 + 1.2

Combine like terms: -1.380821012 + 1.2 = -0.180821012
x = -0.180821012

Simplifying
x = -0.180821012

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.580821012, -0.180821012}
Solution
x = {2.580821012, -0.180821012}