4x(7x-10)=142

Solution for 4x(7x-10)=142 equation:

Simplifying
4x(7x + -10) = 142

Reorder the terms:
4x(-10 + 7x) = 142
(-10 * 4x + 7x * 4x) = 142
(-40x + 28x2) = 142

Solving
-40x + 28x2 = 142

Solving for variable 'x'.

Reorder the terms:
-142 + -40x + 28x2 = 142 + -142

Combine like terms: 142 + -142 = 0
-142 + -40x + 28x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-71 + -20x + 14x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-71 + -20x + 14x2)' equal to zero and attempt to solve:

Simplifying
-71 + -20x + 14x2 = 0

Solving
-71 + -20x + 14x2 = 0

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

Divide each side by '14'.
-5.071428571 + -1.428571429x + x2 = 0

Move the constant term to the right:

Add '5.071428571' to each side of the equation.
-5.071428571 + -1.428571429x + 5.071428571 + x2 = 0 + 5.071428571

Reorder the terms:
-5.071428571 + 5.071428571 + -1.428571429x + x2 = 0 + 5.071428571

Combine like terms: -5.071428571 + 5.071428571 = 0.000000000
0.000000000 + -1.428571429x + x2 = 0 + 5.071428571
-1.428571429x + x2 = 0 + 5.071428571

Combine like terms: 0 + 5.071428571 = 5.071428571
-1.428571429x + x2 = 5.071428571

The x term is -1.428571429x.  Take half its coefficient (-0.7142857145).
Square it (0.5102040819) and add it to both sides.

Add '0.5102040819' to each side of the equation.
-1.428571429x + 0.5102040819 + x2 = 5.071428571 + 0.5102040819

Reorder the terms:
0.5102040819 + -1.428571429x + x2 = 5.071428571 + 0.5102040819

Combine like terms: 5.071428571 + 0.5102040819 = 5.5816326529
0.5102040819 + -1.428571429x + x2 = 5.5816326529

Factor a perfect square on the left side:
(x + -0.7142857145)(x + -0.7142857145) = 5.5816326529

Calculate the square root of the right side: 2.362547915

Break this problem into two subproblems by setting 
(x + -0.7142857145) equal to 2.362547915 and -2.362547915.

Subproblem 1
x + -0.7142857145 = 2.362547915

Simplifying
x + -0.7142857145 = 2.362547915

Reorder the terms:
-0.7142857145 + x = 2.362547915

Solving
-0.7142857145 + x = 2.362547915

Solving for variable 'x'.

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

Add '0.7142857145' to each side of the equation.
-0.7142857145 + 0.7142857145 + x = 2.362547915 + 0.7142857145

Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000
0.0000000000 + x = 2.362547915 + 0.7142857145
x = 2.362547915 + 0.7142857145

Combine like terms: 2.362547915 + 0.7142857145 = 3.0768336295
x = 3.0768336295

Simplifying
x = 3.0768336295

Subproblem 2
x + -0.7142857145 = -2.362547915

Simplifying
x + -0.7142857145 = -2.362547915

Reorder the terms:
-0.7142857145 + x = -2.362547915

Solving
-0.7142857145 + x = -2.362547915

Solving for variable 'x'.

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

Add '0.7142857145' to each side of the equation.
-0.7142857145 + 0.7142857145 + x = -2.362547915 + 0.7142857145

Combine like terms: -0.7142857145 + 0.7142857145 = 0.0000000000
0.0000000000 + x = -2.362547915 + 0.7142857145
x = -2.362547915 + 0.7142857145

Combine like terms: -2.362547915 + 0.7142857145 = -1.6482622005
x = -1.6482622005

Simplifying
x = -1.6482622005

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.0768336295, -1.6482622005}
Solution
x = {3.0768336295, -1.6482622005}