(2x-3)2-(11-x)2+(7-4x)(7+4x)=

Solution for (2x-3)2-(11-x)2+(7-4x)(7+4x)= equation:

Simplifying
(2x + -3) * 2 + -1(11 + -1x) * 2 + (7 + -4x)(7 + 4x) = 0

Reorder the terms:
(-3 + 2x) * 2 + -1(11 + -1x) * 2 + (7 + -4x)(7 + 4x) = 0

Reorder the terms for easier multiplication:
2(-3 + 2x) + -1(11 + -1x) * 2 + (7 + -4x)(7 + 4x) = 0
(-3 * 2 + 2x * 2) + -1(11 + -1x) * 2 + (7 + -4x)(7 + 4x) = 0
(-6 + 4x) + -1(11 + -1x) * 2 + (7 + -4x)(7 + 4x) = 0

Reorder the terms for easier multiplication:
-6 + 4x + -1 * 2(11 + -1x) + (7 + -4x)(7 + 4x) = 0

Multiply -1 * 2
-6 + 4x + -2(11 + -1x) + (7 + -4x)(7 + 4x) = 0
-6 + 4x + (11 * -2 + -1x * -2) + (7 + -4x)(7 + 4x) = 0
-6 + 4x + (-22 + 2x) + (7 + -4x)(7 + 4x) = 0

Multiply (7 + -4x) * (7 + 4x)
-6 + 4x + -22 + 2x + (7(7 + 4x) + -4x * (7 + 4x)) = 0
-6 + 4x + -22 + 2x + ((7 * 7 + 4x * 7) + -4x * (7 + 4x)) = 0
-6 + 4x + -22 + 2x + ((49 + 28x) + -4x * (7 + 4x)) = 0
-6 + 4x + -22 + 2x + (49 + 28x + (7 * -4x + 4x * -4x)) = 0
-6 + 4x + -22 + 2x + (49 + 28x + (-28x + -16x2)) = 0

Combine like terms: 28x + -28x = 0
-6 + 4x + -22 + 2x + (49 + 0 + -16x2) = 0
-6 + 4x + -22 + 2x + (49 + -16x2) = 0

Reorder the terms:
-6 + -22 + 49 + 4x + 2x + -16x2 = 0

Combine like terms: -6 + -22 = -28
-28 + 49 + 4x + 2x + -16x2 = 0

Combine like terms: -28 + 49 = 21
21 + 4x + 2x + -16x2 = 0

Combine like terms: 4x + 2x = 6x
21 + 6x + -16x2 = 0

Solving
21 + 6x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
-1.3125 + -0.375x + x2 = 0

Move the constant term to the right:

Add '1.3125' to each side of the equation.
-1.3125 + -0.375x + 1.3125 + x2 = 0 + 1.3125

Reorder the terms:
-1.3125 + 1.3125 + -0.375x + x2 = 0 + 1.3125

Combine like terms: -1.3125 + 1.3125 = 0.0000
0.0000 + -0.375x + x2 = 0 + 1.3125
-0.375x + x2 = 0 + 1.3125

Combine like terms: 0 + 1.3125 = 1.3125
-0.375x + x2 = 1.3125

The x term is -0.375x.  Take half its coefficient (-0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
-0.375x + 0.03515625 + x2 = 1.3125 + 0.03515625

Reorder the terms:
0.03515625 + -0.375x + x2 = 1.3125 + 0.03515625

Combine like terms: 1.3125 + 0.03515625 = 1.34765625
0.03515625 + -0.375x + x2 = 1.34765625

Factor a perfect square on the left side:
(x + -0.1875)(x + -0.1875) = 1.34765625

Calculate the square root of the right side: 1.160885976

Break this problem into two subproblems by setting 
(x + -0.1875) equal to 1.160885976 and -1.160885976.

Subproblem 1
x + -0.1875 = 1.160885976

Simplifying
x + -0.1875 = 1.160885976

Reorder the terms:
-0.1875 + x = 1.160885976

Solving
-0.1875 + x = 1.160885976

Solving for variable 'x'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + x = 1.160885976 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + x = 1.160885976 + 0.1875
x = 1.160885976 + 0.1875

Combine like terms: 1.160885976 + 0.1875 = 1.348385976
x = 1.348385976

Simplifying
x = 1.348385976

Subproblem 2
x + -0.1875 = -1.160885976

Simplifying
x + -0.1875 = -1.160885976

Reorder the terms:
-0.1875 + x = -1.160885976

Solving
-0.1875 + x = -1.160885976

Solving for variable 'x'.

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

Add '0.1875' to each side of the equation.
-0.1875 + 0.1875 + x = -1.160885976 + 0.1875

Combine like terms: -0.1875 + 0.1875 = 0.0000
0.0000 + x = -1.160885976 + 0.1875
x = -1.160885976 + 0.1875

Combine like terms: -1.160885976 + 0.1875 = -0.973385976
x = -0.973385976

Simplifying
x = -0.973385976

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.348385976, -0.973385976}