(x)(4x+7)=360

Solution for (x)(4x+7)=360 equation:

Simplifying
(x)(4x + 7) = 360

Reorder the terms:
x(7 + 4x) = 360
(7 * x + 4x * x) = 360
(7x + 4x2) = 360

Solving
7x + 4x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 7x + 4x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 7x + 4x2 = 0

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

Divide each side by '4'.
-90 + 1.75x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 1.75x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 1.75x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 1.75x + x2 = 0 + 90
1.75x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
1.75x + x2 = 90

The x term is 1.75x.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75x + 0.765625 + x2 = 90 + 0.765625

Reorder the terms:
0.765625 + 1.75x + x2 = 90 + 0.765625

Combine like terms: 90 + 0.765625 = 90.765625
0.765625 + 1.75x + x2 = 90.765625

Factor a perfect square on the left side:
(x + 0.875)(x + 0.875) = 90.765625

Calculate the square root of the right side: 9.527099506

Break this problem into two subproblems by setting 
(x + 0.875) equal to 9.527099506 and -9.527099506.

Subproblem 1
x + 0.875 = 9.527099506

Simplifying
x + 0.875 = 9.527099506

Reorder the terms:
0.875 + x = 9.527099506

Solving
0.875 + x = 9.527099506

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = 9.527099506 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = 9.527099506 + -0.875
x = 9.527099506 + -0.875

Combine like terms: 9.527099506 + -0.875 = 8.652099506
x = 8.652099506

Simplifying
x = 8.652099506

Subproblem 2
x + 0.875 = -9.527099506

Simplifying
x + 0.875 = -9.527099506

Reorder the terms:
0.875 + x = -9.527099506

Solving
0.875 + x = -9.527099506

Solving for variable 'x'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + x = -9.527099506 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + x = -9.527099506 + -0.875
x = -9.527099506 + -0.875

Combine like terms: -9.527099506 + -0.875 = -10.402099506
x = -10.402099506

Simplifying
x = -10.402099506

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.652099506, -10.402099506}