4x(2x+42)=180

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Solution for 4x(2x+42)=180 equation: 


Simplifying
4x(2x + 42) = 180

Reorder the terms:
4x(42 + 2x) = 180
(42 * 4x + 2x * 4x) = 180
(168x + 8x2) = 180

Solving
168x + 8x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 168x + 8x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 168x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 42x + 2x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + 42x + 2x2)' equal to zero and attempt to solve:

Simplifying
-45 + 42x + 2x2 = 0

Solving
-45 + 42x + 2x2 = 0

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

Divide each side by '2'.
-22.5 + 21x + x2 = 0

Move the constant term to the right:

Add '22.5' to each side of the equation.
-22.5 + 21x + 22.5 + x2 = 0 + 22.5

Reorder the terms:
-22.5 + 22.5 + 21x + x2 = 0 + 22.5

Combine like terms: -22.5 + 22.5 = 0.0
0.0 + 21x + x2 = 0 + 22.5
21x + x2 = 0 + 22.5

Combine like terms: 0 + 22.5 = 22.5
21x + x2 = 22.5

The x term is 21x.  Take half its coefficient (10.5).
Square it (110.25) and add it to both sides.

Add '110.25' to each side of the equation.
21x + 110.25 + x2 = 22.5 + 110.25

Reorder the terms:
110.25 + 21x + x2 = 22.5 + 110.25

Combine like terms: 22.5 + 110.25 = 132.75
110.25 + 21x + x2 = 132.75

Factor a perfect square on the left side:
(x + 10.5)(x + 10.5) = 132.75

Calculate the square root of the right side: 11.521718622

Break this problem into two subproblems by setting 
(x + 10.5) equal to 11.521718622 and -11.521718622.


Subproblem 1
x + 10.5 = 11.521718622

Simplifying
x + 10.5 = 11.521718622

Reorder the terms:
10.5 + x = 11.521718622

Solving
10.5 + x = 11.521718622

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = 11.521718622 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = 11.521718622 + -10.5
x = 11.521718622 + -10.5

Combine like terms: 11.521718622 + -10.5 = 1.021718622
x = 1.021718622

Simplifying
x = 1.021718622


Subproblem 2
x + 10.5 = -11.521718622

Simplifying
x + 10.5 = -11.521718622

Reorder the terms:
10.5 + x = -11.521718622

Solving
10.5 + x = -11.521718622

Solving for variable 'x'.

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

Add '-10.5' to each side of the equation.
10.5 + -10.5 + x = -11.521718622 + -10.5

Combine like terms: 10.5 + -10.5 = 0.0
0.0 + x = -11.521718622 + -10.5
x = -11.521718622 + -10.5

Combine like terms: -11.521718622 + -10.5 = -22.021718622
x = -22.021718622

Simplifying
x = -22.021718622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.021718622, -22.021718622}
Solution
x = {1.021718622, -22.021718622}

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