(2x-7)(x+4)=42

Solution for (2x-7)(x+4)=42 equation:

Simplifying
(2x + -7)(x + 4) = 42

Reorder the terms:
(-7 + 2x)(x + 4) = 42

Reorder the terms:
(-7 + 2x)(4 + x) = 42

Multiply (-7 + 2x) * (4 + x)
(-7(4 + x) + 2x * (4 + x)) = 42
((4 * -7 + x * -7) + 2x * (4 + x)) = 42
((-28 + -7x) + 2x * (4 + x)) = 42
(-28 + -7x + (4 * 2x + x * 2x)) = 42
(-28 + -7x + (8x + 2x2)) = 42

Combine like terms: -7x + 8x = 1x
(-28 + 1x + 2x2) = 42

Solving
-28 + 1x + 2x2 = 42

Solving for variable 'x'.

Reorder the terms:
-28 + -42 + 1x + 2x2 = 42 + -42

Combine like terms: -28 + -42 = -70
-70 + 1x + 2x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-70 + 1x + 2x2 = 0

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

Divide each side by '2'.
-35 + 0.5x + x2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + 0.5x + 35 + x2 = 0 + 35

Reorder the terms:
-35 + 35 + 0.5x + x2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + 0.5x + x2 = 0 + 35
0.5x + x2 = 0 + 35

Combine like terms: 0 + 35 = 35
0.5x + x2 = 35

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 35 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 35 + 0.0625

Combine like terms: 35 + 0.0625 = 35.0625
0.0625 + 0.5x + x2 = 35.0625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 35.0625

Calculate the square root of the right side: 5.921359641

Break this problem into two subproblems by setting 
(x + 0.25) equal to 5.921359641 and -5.921359641.

Subproblem 1
x + 0.25 = 5.921359641

Simplifying
x + 0.25 = 5.921359641

Reorder the terms:
0.25 + x = 5.921359641

Solving
0.25 + x = 5.921359641

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 5.921359641 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 5.921359641 + -0.25
x = 5.921359641 + -0.25

Combine like terms: 5.921359641 + -0.25 = 5.671359641
x = 5.671359641

Simplifying
x = 5.671359641

Subproblem 2
x + 0.25 = -5.921359641

Simplifying
x + 0.25 = -5.921359641

Reorder the terms:
0.25 + x = -5.921359641

Solving
0.25 + x = -5.921359641

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -5.921359641 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -5.921359641 + -0.25
x = -5.921359641 + -0.25

Combine like terms: -5.921359641 + -0.25 = -6.171359641
x = -6.171359641

Simplifying
x = -6.171359641

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.671359641, -6.171359641}