-4x-7=5x(x+21)

Solution for -4x-7=5x(x+21) equation:

Simplifying
-4x + -7 = 5x(x + 21)

Reorder the terms:
-7 + -4x = 5x(x + 21)

Reorder the terms:
-7 + -4x = 5x(21 + x)
-7 + -4x = (21 * 5x + x * 5x)
-7 + -4x = (105x + 5x2)

Solving
-7 + -4x = 105x + 5x2

Solving for variable 'x'.

Combine like terms: -4x + -105x = -109x
-7 + -109x + -5x2 = 105x + 5x2 + -105x + -5x2

Reorder the terms:
-7 + -109x + -5x2 = 105x + -105x + 5x2 + -5x2

Combine like terms: 105x + -105x = 0
-7 + -109x + -5x2 = 0 + 5x2 + -5x2
-7 + -109x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-7 + -109x + -5x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 109x + 5x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(7 + 109x + 5x2)' equal to zero and attempt to solve:

Simplifying
7 + 109x + 5x2 = 0

Solving
7 + 109x + 5x2 = 0

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

Divide each side by '5'.
1.4 + 21.8x + x2 = 0

Move the constant term to the right:

Add '-1.4' to each side of the equation.
1.4 + 21.8x + -1.4 + x2 = 0 + -1.4

Reorder the terms:
1.4 + -1.4 + 21.8x + x2 = 0 + -1.4

Combine like terms: 1.4 + -1.4 = 0.0
0.0 + 21.8x + x2 = 0 + -1.4
21.8x + x2 = 0 + -1.4

Combine like terms: 0 + -1.4 = -1.4
21.8x + x2 = -1.4

The x term is 21.8x.  Take half its coefficient (10.9).
Square it (118.81) and add it to both sides.

Add '118.81' to each side of the equation.
21.8x + 118.81 + x2 = -1.4 + 118.81

Reorder the terms:
118.81 + 21.8x + x2 = -1.4 + 118.81

Combine like terms: -1.4 + 118.81 = 117.41
118.81 + 21.8x + x2 = 117.41

Factor a perfect square on the left side:
(x + 10.9)(x + 10.9) = 117.41

Calculate the square root of the right side: 10.835589509

Break this problem into two subproblems by setting 
(x + 10.9) equal to 10.835589509 and -10.835589509.

Subproblem 1
x + 10.9 = 10.835589509

Simplifying
x + 10.9 = 10.835589509

Reorder the terms:
10.9 + x = 10.835589509

Solving
10.9 + x = 10.835589509

Solving for variable 'x'.

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

Add '-10.9' to each side of the equation.
10.9 + -10.9 + x = 10.835589509 + -10.9

Combine like terms: 10.9 + -10.9 = 0.0
0.0 + x = 10.835589509 + -10.9
x = 10.835589509 + -10.9

Combine like terms: 10.835589509 + -10.9 = -0.064410491
x = -0.064410491

Simplifying
x = -0.064410491

Subproblem 2
x + 10.9 = -10.835589509

Simplifying
x + 10.9 = -10.835589509

Reorder the terms:
10.9 + x = -10.835589509

Solving
10.9 + x = -10.835589509

Solving for variable 'x'.

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

Add '-10.9' to each side of the equation.
10.9 + -10.9 + x = -10.835589509 + -10.9

Combine like terms: 10.9 + -10.9 = 0.0
0.0 + x = -10.835589509 + -10.9
x = -10.835589509 + -10.9

Combine like terms: -10.835589509 + -10.9 = -21.735589509
x = -21.735589509

Simplifying
x = -21.735589509

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.064410491, -21.735589509}
Solution
x = {-0.064410491, -21.735589509}