7x(3x+24)=180

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Solution for 7x(3x+24)=180 equation: 


Simplifying
7x(3x + 24) = 180

Reorder the terms:
7x(24 + 3x) = 180
(24 * 7x + 3x * 7x) = 180
(168x + 21x2) = 180

Solving
168x + 21x2 = 180

Solving for variable 'x'.

Reorder the terms:
-180 + 168x + 21x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 168x + 21x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-60 + 56x + 7x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-60 + 56x + 7x2)' equal to zero and attempt to solve:

Simplifying
-60 + 56x + 7x2 = 0

Solving
-60 + 56x + 7x2 = 0

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

Divide each side by '7'.
-8.571428571 + 8x + x2 = 0

Move the constant term to the right:

Add '8.571428571' to each side of the equation.
-8.571428571 + 8x + 8.571428571 + x2 = 0 + 8.571428571

Reorder the terms:
-8.571428571 + 8.571428571 + 8x + x2 = 0 + 8.571428571

Combine like terms: -8.571428571 + 8.571428571 = 0.000000000
0.000000000 + 8x + x2 = 0 + 8.571428571
8x + x2 = 0 + 8.571428571

Combine like terms: 0 + 8.571428571 = 8.571428571
8x + x2 = 8.571428571

The x term is 8x.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8x + 16 + x2 = 8.571428571 + 16

Reorder the terms:
16 + 8x + x2 = 8.571428571 + 16

Combine like terms: 8.571428571 + 16 = 24.571428571
16 + 8x + x2 = 24.571428571

Factor a perfect square on the left side:
(x + 4)(x + 4) = 24.571428571

Calculate the square root of the right side: 4.956957592

Break this problem into two subproblems by setting 
(x + 4) equal to 4.956957592 and -4.956957592.


Subproblem 1
x + 4 = 4.956957592

Simplifying
x + 4 = 4.956957592

Reorder the terms:
4 + x = 4.956957592

Solving
4 + x = 4.956957592

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = 4.956957592 + -4

Combine like terms: 4 + -4 = 0
0 + x = 4.956957592 + -4
x = 4.956957592 + -4

Combine like terms: 4.956957592 + -4 = 0.956957592
x = 0.956957592

Simplifying
x = 0.956957592


Subproblem 2
x + 4 = -4.956957592

Simplifying
x + 4 = -4.956957592

Reorder the terms:
4 + x = -4.956957592

Solving
4 + x = -4.956957592

Solving for variable 'x'.

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

Add '-4' to each side of the equation.
4 + -4 + x = -4.956957592 + -4

Combine like terms: 4 + -4 = 0
0 + x = -4.956957592 + -4
x = -4.956957592 + -4

Combine like terms: -4.956957592 + -4 = -8.956957592
x = -8.956957592

Simplifying
x = -8.956957592


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.956957592, -8.956957592}
Solution
x = {0.956957592, -8.956957592}

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