4x(x-2)=42

Solution for 4x(x-2)=42 equation:

Simplifying
4x(x + -2) = 42

Reorder the terms:
4x(-2 + x) = 42
(-2 * 4x + x * 4x) = 42
(-8x + 4x2) = 42

Solving
-8x + 4x2 = 42

Solving for variable 'x'.

Reorder the terms:
-42 + -8x + 4x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + -8x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-21 + -4x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-21 + -4x + 2x2)' equal to zero and attempt to solve:

Simplifying
-21 + -4x + 2x2 = 0

Solving
-21 + -4x + 2x2 = 0

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

Divide each side by '2'.
-10.5 + -2x + x2 = 0

Move the constant term to the right:

Add '10.5' to each side of the equation.
-10.5 + -2x + 10.5 + x2 = 0 + 10.5

Reorder the terms:
-10.5 + 10.5 + -2x + x2 = 0 + 10.5

Combine like terms: -10.5 + 10.5 = 0.0
0.0 + -2x + x2 = 0 + 10.5
-2x + x2 = 0 + 10.5

Combine like terms: 0 + 10.5 = 10.5
-2x + x2 = 10.5

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 = 10.5 + 1

Reorder the terms:
1 + -2x + x2 = 10.5 + 1

Combine like terms: 10.5 + 1 = 11.5
1 + -2x + x2 = 11.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 11.5

Calculate the square root of the right side: 3.391164992

Break this problem into two subproblems by setting 
(x + -1) equal to 3.391164992 and -3.391164992.

Subproblem 1
x + -1 = 3.391164992

Simplifying
x + -1 = 3.391164992

Reorder the terms:
-1 + x = 3.391164992

Solving
-1 + x = 3.391164992

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 = 3.391164992 + 1

Combine like terms: -1 + 1 = 0
0 + x = 3.391164992 + 1
x = 3.391164992 + 1

Combine like terms: 3.391164992 + 1 = 4.391164992
x = 4.391164992

Simplifying
x = 4.391164992

Subproblem 2
x + -1 = -3.391164992

Simplifying
x + -1 = -3.391164992

Reorder the terms:
-1 + x = -3.391164992

Solving
-1 + x = -3.391164992

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 = -3.391164992 + 1

Combine like terms: -1 + 1 = 0
0 + x = -3.391164992 + 1
x = -3.391164992 + 1

Combine like terms: -3.391164992 + 1 = -2.391164992
x = -2.391164992

Simplifying
x = -2.391164992

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.391164992, -2.391164992}
Solution
x = {4.391164992, -2.391164992}