(2x+10)(2x-7)=342-4x^2

Solution for (2x+10)(2x-7)=342-4x^2 equation:

Simplifying
(2x + 10)(2x + -7) = 342 + -4x2

Reorder the terms:
(10 + 2x)(2x + -7) = 342 + -4x2

Reorder the terms:
(10 + 2x)(-7 + 2x) = 342 + -4x2

Multiply (10 + 2x) * (-7 + 2x)
(10(-7 + 2x) + 2x * (-7 + 2x)) = 342 + -4x2
((-7 * 10 + 2x * 10) + 2x * (-7 + 2x)) = 342 + -4x2
((-70 + 20x) + 2x * (-7 + 2x)) = 342 + -4x2
(-70 + 20x + (-7 * 2x + 2x * 2x)) = 342 + -4x2
(-70 + 20x + (-14x + 4x2)) = 342 + -4x2

Combine like terms: 20x + -14x = 6x
(-70 + 6x + 4x2) = 342 + -4x2

Solving
-70 + 6x + 4x2 = 342 + -4x2

Solving for variable 'x'.

Reorder the terms:
-70 + -342 + 6x + 4x2 + 4x2 = 342 + -4x2 + -342 + 4x2

Combine like terms: -70 + -342 = -412
-412 + 6x + 4x2 + 4x2 = 342 + -4x2 + -342 + 4x2

Combine like terms: 4x2 + 4x2 = 8x2
-412 + 6x + 8x2 = 342 + -4x2 + -342 + 4x2

Reorder the terms:
-412 + 6x + 8x2 = 342 + -342 + -4x2 + 4x2

Combine like terms: 342 + -342 = 0
-412 + 6x + 8x2 = 0 + -4x2 + 4x2
-412 + 6x + 8x2 = -4x2 + 4x2

Combine like terms: -4x2 + 4x2 = 0
-412 + 6x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-206 + 3x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-206 + 3x + 4x2)' equal to zero and attempt to solve:

Simplifying
-206 + 3x + 4x2 = 0

Solving
-206 + 3x + 4x2 = 0

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

Divide each side by '4'.
-51.5 + 0.75x + x2 = 0

Move the constant term to the right:

Add '51.5' to each side of the equation.
-51.5 + 0.75x + 51.5 + x2 = 0 + 51.5

Reorder the terms:
-51.5 + 51.5 + 0.75x + x2 = 0 + 51.5

Combine like terms: -51.5 + 51.5 = 0.0
0.0 + 0.75x + x2 = 0 + 51.5
0.75x + x2 = 0 + 51.5

Combine like terms: 0 + 51.5 = 51.5
0.75x + x2 = 51.5

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 51.5 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 51.5 + 0.140625

Combine like terms: 51.5 + 0.140625 = 51.640625
0.140625 + 0.75x + x2 = 51.640625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 51.640625

Calculate the square root of the right side: 7.186141176

Break this problem into two subproblems by setting 
(x + 0.375) equal to 7.186141176 and -7.186141176.

Subproblem 1
x + 0.375 = 7.186141176

Simplifying
x + 0.375 = 7.186141176

Reorder the terms:
0.375 + x = 7.186141176

Solving
0.375 + x = 7.186141176

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 7.186141176 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 7.186141176 + -0.375
x = 7.186141176 + -0.375

Combine like terms: 7.186141176 + -0.375 = 6.811141176
x = 6.811141176

Simplifying
x = 6.811141176

Subproblem 2
x + 0.375 = -7.186141176

Simplifying
x + 0.375 = -7.186141176

Reorder the terms:
0.375 + x = -7.186141176

Solving
0.375 + x = -7.186141176

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -7.186141176 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -7.186141176 + -0.375
x = -7.186141176 + -0.375

Combine like terms: -7.186141176 + -0.375 = -7.561141176
x = -7.561141176

Simplifying
x = -7.561141176

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.811141176, -7.561141176}
Solution
x = {6.811141176, -7.561141176}