(x)(4x+3)=360

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Solution for (x)(4x+3)=360 equation: 


Simplifying
(x)(4x + 3) = 360

Reorder the terms:
x(3 + 4x) = 360
(3 * x + 4x * x) = 360
(3x + 4x2) = 360

Solving
3x + 4x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + 3x + 4x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + 3x + 4x2 = 0

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

Divide each side by '4'.
-90 + 0.75x + x2 = 0

Move the constant term to the right:

Add '90' to each side of the equation.
-90 + 0.75x + 90 + x2 = 0 + 90

Reorder the terms:
-90 + 90 + 0.75x + x2 = 0 + 90

Combine like terms: -90 + 90 = 0
0 + 0.75x + x2 = 0 + 90
0.75x + x2 = 0 + 90

Combine like terms: 0 + 90 = 90
0.75x + x2 = 90

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 = 90 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 90 + 0.140625

Combine like terms: 90 + 0.140625 = 90.140625
0.140625 + 0.75x + x2 = 90.140625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 90.140625

Calculate the square root of the right side: 9.494241676

Break this problem into two subproblems by setting 
(x + 0.375) equal to 9.494241676 and -9.494241676.


Subproblem 1
x + 0.375 = 9.494241676

Simplifying
x + 0.375 = 9.494241676

Reorder the terms:
0.375 + x = 9.494241676

Solving
0.375 + x = 9.494241676

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 = 9.494241676 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 9.494241676 + -0.375
x = 9.494241676 + -0.375

Combine like terms: 9.494241676 + -0.375 = 9.119241676
x = 9.119241676

Simplifying
x = 9.119241676


Subproblem 2
x + 0.375 = -9.494241676

Simplifying
x + 0.375 = -9.494241676

Reorder the terms:
0.375 + x = -9.494241676

Solving
0.375 + x = -9.494241676

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 = -9.494241676 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -9.494241676 + -0.375
x = -9.494241676 + -0.375

Combine like terms: -9.494241676 + -0.375 = -9.869241676
x = -9.869241676

Simplifying
x = -9.869241676


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.119241676, -9.869241676}

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