(4x)(x+6)=180

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Solution for (4x)(x+6)=180 equation: 


Simplifying
(4x)(x + 6) = 180

Remove parenthesis around (4x)
4x(x + 6) = 180

Reorder the terms:
4x(6 + x) = 180
(6 * 4x + x * 4x) = 180
(24x + 4x2) = 180

Solving
24x + 4x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 24x + 4x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 24x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-45 + 6x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-45 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-45 + 6x + x2 = 0

Solving
-45 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '45' to each side of the equation.
-45 + 6x + 45 + x2 = 0 + 45

Reorder the terms:
-45 + 45 + 6x + x2 = 0 + 45

Combine like terms: -45 + 45 = 0
0 + 6x + x2 = 0 + 45
6x + x2 = 0 + 45

Combine like terms: 0 + 45 = 45
6x + x2 = 45

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 45 + 9

Reorder the terms:
9 + 6x + x2 = 45 + 9

Combine like terms: 45 + 9 = 54
9 + 6x + x2 = 54

Factor a perfect square on the left side:
(x + 3)(x + 3) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(x + 3) equal to 7.348469228 and -7.348469228.


Subproblem 1
x + 3 = 7.348469228

Simplifying
x + 3 = 7.348469228

Reorder the terms:
3 + x = 7.348469228

Solving
3 + x = 7.348469228

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = 7.348469228 + -3

Combine like terms: 3 + -3 = 0
0 + x = 7.348469228 + -3
x = 7.348469228 + -3

Combine like terms: 7.348469228 + -3 = 4.348469228
x = 4.348469228

Simplifying
x = 4.348469228


Subproblem 2
x + 3 = -7.348469228

Simplifying
x + 3 = -7.348469228

Reorder the terms:
3 + x = -7.348469228

Solving
3 + x = -7.348469228

Solving for variable 'x'.

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

Add '-3' to each side of the equation.
3 + -3 + x = -7.348469228 + -3

Combine like terms: 3 + -3 = 0
0 + x = -7.348469228 + -3
x = -7.348469228 + -3

Combine like terms: -7.348469228 + -3 = -10.348469228
x = -10.348469228

Simplifying
x = -10.348469228


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.348469228, -10.348469228}
Solution
x = {4.348469228, -10.348469228}

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