(7x-16)=4x(x+8)

Solution for (7x-16)=4x(x+8) equation:

Simplifying
(7x + -16) = 4x(x + 8)

Reorder the terms:
(-16 + 7x) = 4x(x + 8)

Remove parenthesis around (-16 + 7x)
-16 + 7x = 4x(x + 8)

Reorder the terms:
-16 + 7x = 4x(8 + x)
-16 + 7x = (8 * 4x + x * 4x)
-16 + 7x = (32x + 4x2)

Solving
-16 + 7x = 32x + 4x2

Solving for variable 'x'.

Combine like terms: 7x + -32x = -25x
-16 + -25x + -4x2 = 32x + 4x2 + -32x + -4x2

Reorder the terms:
-16 + -25x + -4x2 = 32x + -32x + 4x2 + -4x2

Combine like terms: 32x + -32x = 0
-16 + -25x + -4x2 = 0 + 4x2 + -4x2
-16 + -25x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-16 + -25x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(16 + 25x + 4x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(16 + 25x + 4x2)' equal to zero and attempt to solve:

Simplifying
16 + 25x + 4x2 = 0

Solving
16 + 25x + 4x2 = 0

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

Divide each side by '4'.
4 + 6.25x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 6.25x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 6.25x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 6.25x + x2 = 0 + -4
6.25x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
6.25x + x2 = -4

The x term is 6.25x.  Take half its coefficient (3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
6.25x + 9.765625 + x2 = -4 + 9.765625

Reorder the terms:
9.765625 + 6.25x + x2 = -4 + 9.765625

Combine like terms: -4 + 9.765625 = 5.765625
9.765625 + 6.25x + x2 = 5.765625

Factor a perfect square on the left side:
(x + 3.125)(x + 3.125) = 5.765625

Calculate the square root of the right side: 2.401171589

Break this problem into two subproblems by setting 
(x + 3.125) equal to 2.401171589 and -2.401171589.

Subproblem 1
x + 3.125 = 2.401171589

Simplifying
x + 3.125 = 2.401171589

Reorder the terms:
3.125 + x = 2.401171589

Solving
3.125 + x = 2.401171589

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = 2.401171589 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = 2.401171589 + -3.125
x = 2.401171589 + -3.125

Combine like terms: 2.401171589 + -3.125 = -0.723828411
x = -0.723828411

Simplifying
x = -0.723828411

Subproblem 2
x + 3.125 = -2.401171589

Simplifying
x + 3.125 = -2.401171589

Reorder the terms:
3.125 + x = -2.401171589

Solving
3.125 + x = -2.401171589

Solving for variable 'x'.

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

Add '-3.125' to each side of the equation.
3.125 + -3.125 + x = -2.401171589 + -3.125

Combine like terms: 3.125 + -3.125 = 0.000
0.000 + x = -2.401171589 + -3.125
x = -2.401171589 + -3.125

Combine like terms: -2.401171589 + -3.125 = -5.526171589
x = -5.526171589

Simplifying
x = -5.526171589

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.723828411, -5.526171589}
Solution
x = {-0.723828411, -5.526171589}