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

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

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

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

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

Reorder the terms for easier multiplication:
42 = 2 * 2(4 + x)(-7 + 2x)

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

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

Combine like terms: 8x + -7x = 1x
42 = 4(-28 + 1x + 2x2)
42 = (-28 * 4 + 1x * 4 + 2x2 * 4)
42 = (-112 + 4x + 8x2)

Solving
42 = -112 + 4x + 8x2

Solving for variable 'x'.

Combine like terms: 42 + 112 = 154
154 + -4x + -8x2 = -112 + 4x + 8x2 + 112 + -4x + -8x2

Reorder the terms:
154 + -4x + -8x2 = -112 + 112 + 4x + -4x + 8x2 + -8x2

Combine like terms: -112 + 112 = 0
154 + -4x + -8x2 = 0 + 4x + -4x + 8x2 + -8x2
154 + -4x + -8x2 = 4x + -4x + 8x2 + -8x2

Combine like terms: 4x + -4x = 0
154 + -4x + -8x2 = 0 + 8x2 + -8x2
154 + -4x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
154 + -4x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(77 + -2x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(77 + -2x + -4x2)' equal to zero and attempt to solve:

Simplifying
77 + -2x + -4x2 = 0

Solving
77 + -2x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-19.25 + 0.5x + x2 = 0

Move the constant term to the right:

Add '19.25' to each side of the equation.
-19.25 + 0.5x + 19.25 + x2 = 0 + 19.25

Reorder the terms:
-19.25 + 19.25 + 0.5x + x2 = 0 + 19.25

Combine like terms: -19.25 + 19.25 = 0.00
0.00 + 0.5x + x2 = 0 + 19.25
0.5x + x2 = 0 + 19.25

Combine like terms: 0 + 19.25 = 19.25
0.5x + x2 = 19.25

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 = 19.25 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 19.25 + 0.0625

Combine like terms: 19.25 + 0.0625 = 19.3125
0.0625 + 0.5x + x2 = 19.3125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 19.3125

Calculate the square root of the right side: 4.394598958

Break this problem into two subproblems by setting 
(x + 0.25) equal to 4.394598958 and -4.394598958.

Subproblem 1
x + 0.25 = 4.394598958

Simplifying
x + 0.25 = 4.394598958

Reorder the terms:
0.25 + x = 4.394598958

Solving
0.25 + x = 4.394598958

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 = 4.394598958 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 4.394598958 + -0.25
x = 4.394598958 + -0.25

Combine like terms: 4.394598958 + -0.25 = 4.144598958
x = 4.144598958

Simplifying
x = 4.144598958

Subproblem 2
x + 0.25 = -4.394598958

Simplifying
x + 0.25 = -4.394598958

Reorder the terms:
0.25 + x = -4.394598958

Solving
0.25 + x = -4.394598958

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 = -4.394598958 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -4.394598958 + -0.25
x = -4.394598958 + -0.25

Combine like terms: -4.394598958 + -0.25 = -4.644598958
x = -4.644598958

Simplifying
x = -4.644598958

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.144598958, -4.644598958}
Solution
x = {4.144598958, -4.644598958}