7(x-2)14x=10

Solution for 7(x-2)14x=10 equation:

Simplifying
7(x + -2) * 14x = 10

Reorder the terms:
7(-2 + x) * 14x = 10

Reorder the terms for easier multiplication:
7 * 14x(-2 + x) = 10

Multiply 7 * 14
98x(-2 + x) = 10
(-2 * 98x + x * 98x) = 10
(-196x + 98x2) = 10

Solving
-196x + 98x2 = 10

Solving for variable 'x'.

Reorder the terms:
-10 + -196x + 98x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + -196x + 98x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -98x + 49x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -98x + 49x2)' equal to zero and attempt to solve:

Simplifying
-5 + -98x + 49x2 = 0

Solving
-5 + -98x + 49x2 = 0

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

Divide each side by '49'.
-0.1020408163 + -2x + x2 = 0

Move the constant term to the right:

Add '0.1020408163' to each side of the equation.
-0.1020408163 + -2x + 0.1020408163 + x2 = 0 + 0.1020408163

Reorder the terms:
-0.1020408163 + 0.1020408163 + -2x + x2 = 0 + 0.1020408163

Combine like terms: -0.1020408163 + 0.1020408163 = 0.0000000000
0.0000000000 + -2x + x2 = 0 + 0.1020408163
-2x + x2 = 0 + 0.1020408163

Combine like terms: 0 + 0.1020408163 = 0.1020408163
-2x + x2 = 0.1020408163

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 0.1020408163 + 1

Reorder the terms:
1 + -2x + x2 = 0.1020408163 + 1

Combine like terms: 0.1020408163 + 1 = 1.1020408163
1 + -2x + x2 = 1.1020408163

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.1020408163

Calculate the square root of the right side: 1.049781318

Break this problem into two subproblems by setting 
(x + -1) equal to 1.049781318 and -1.049781318.

Subproblem 1
x + -1 = 1.049781318

Simplifying
x + -1 = 1.049781318

Reorder the terms:
-1 + x = 1.049781318

Solving
-1 + x = 1.049781318

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.049781318 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.049781318 + 1
x = 1.049781318 + 1

Combine like terms: 1.049781318 + 1 = 2.049781318
x = 2.049781318

Simplifying
x = 2.049781318

Subproblem 2
x + -1 = -1.049781318

Simplifying
x + -1 = -1.049781318

Reorder the terms:
-1 + x = -1.049781318

Solving
-1 + x = -1.049781318

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.049781318 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.049781318 + 1
x = -1.049781318 + 1

Combine like terms: -1.049781318 + 1 = -0.049781318
x = -0.049781318

Simplifying
x = -0.049781318

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.049781318, -0.049781318}
Solution
x = {2.049781318, -0.049781318}