(4x+6)5x+113+90=540

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Solution for (4x+6)5x+113+90=540 equation: 


Simplifying
(4x + 6) * 5x + 113 + 90 = 540

Reorder the terms:
(6 + 4x) * 5x + 113 + 90 = 540

Reorder the terms for easier multiplication:
5x(6 + 4x) + 113 + 90 = 540
(6 * 5x + 4x * 5x) + 113 + 90 = 540
(30x + 20x2) + 113 + 90 = 540

Reorder the terms:
113 + 90 + 30x + 20x2 = 540

Combine like terms: 113 + 90 = 203
203 + 30x + 20x2 = 540

Solving
203 + 30x + 20x2 = 540

Solving for variable 'x'.

Reorder the terms:
203 + -540 + 30x + 20x2 = 540 + -540

Combine like terms: 203 + -540 = -337
-337 + 30x + 20x2 = 540 + -540

Combine like terms: 540 + -540 = 0
-337 + 30x + 20x2 = 0

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

Divide each side by '20'.
-16.85 + 1.5x + x2 = 0.0

Move the constant term to the right:

Add '16.85' to each side of the equation.
-16.85 + 1.5x + 16.85 + x2 = 0.0 + 16.85

Reorder the terms:
-16.85 + 16.85 + 1.5x + x2 = 0.0 + 16.85

Combine like terms: -16.85 + 16.85 = 0.00
0.00 + 1.5x + x2 = 0.0 + 16.85
1.5x + x2 = 0.0 + 16.85

Combine like terms: 0.0 + 16.85 = 16.85
1.5x + x2 = 16.85

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 16.85 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 16.85 + 0.5625

Combine like terms: 16.85 + 0.5625 = 17.4125
0.5625 + 1.5x + x2 = 17.4125

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 17.4125

Calculate the square root of the right side: 4.172828777

Break this problem into two subproblems by setting 
(x + 0.75) equal to 4.172828777 and -4.172828777.


Subproblem 1
x + 0.75 = 4.172828777

Simplifying
x + 0.75 = 4.172828777

Reorder the terms:
0.75 + x = 4.172828777

Solving
0.75 + x = 4.172828777

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 4.172828777 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 4.172828777 + -0.75
x = 4.172828777 + -0.75

Combine like terms: 4.172828777 + -0.75 = 3.422828777
x = 3.422828777

Simplifying
x = 3.422828777


Subproblem 2
x + 0.75 = -4.172828777

Simplifying
x + 0.75 = -4.172828777

Reorder the terms:
0.75 + x = -4.172828777

Solving
0.75 + x = -4.172828777

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -4.172828777 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -4.172828777 + -0.75
x = -4.172828777 + -0.75

Combine like terms: -4.172828777 + -0.75 = -4.922828777
x = -4.922828777

Simplifying
x = -4.922828777


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.422828777, -4.922828777}

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