-12(x+3)=4x(x-21)

Solution for -12(x+3)=4x(x-21) equation:

Simplifying
-12(x + 3) = 4x(x + -21)

Reorder the terms:
-12(3 + x) = 4x(x + -21)
(3 * -12 + x * -12) = 4x(x + -21)
(-36 + -12x) = 4x(x + -21)

Reorder the terms:
-36 + -12x = 4x(-21 + x)
-36 + -12x = (-21 * 4x + x * 4x)
-36 + -12x = (-84x + 4x2)

Solving
-36 + -12x = -84x + 4x2

Solving for variable 'x'.

Combine like terms: -12x + 84x = 72x
-36 + 72x + -4x2 = -84x + 4x2 + 84x + -4x2

Reorder the terms:
-36 + 72x + -4x2 = -84x + 84x + 4x2 + -4x2

Combine like terms: -84x + 84x = 0
-36 + 72x + -4x2 = 0 + 4x2 + -4x2
-36 + 72x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-36 + 72x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-9 + 18x + -1x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-9 + 18x + -1x2)' equal to zero and attempt to solve:

Simplifying
-9 + 18x + -1x2 = 0

Solving
-9 + 18x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
9 + -18x + x2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -18x + -9 + x2 = 0 + -9

Reorder the terms:
9 + -9 + -18x + x2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -18x + x2 = 0 + -9
-18x + x2 = 0 + -9

Combine like terms: 0 + -9 = -9
-18x + x2 = -9

The x term is -18x.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18x + 81 + x2 = -9 + 81

Reorder the terms:
81 + -18x + x2 = -9 + 81

Combine like terms: -9 + 81 = 72
81 + -18x + x2 = 72

Factor a perfect square on the left side:
(x + -9)(x + -9) = 72

Calculate the square root of the right side: 8.485281374

Break this problem into two subproblems by setting 
(x + -9) equal to 8.485281374 and -8.485281374.

Subproblem 1
x + -9 = 8.485281374

Simplifying
x + -9 = 8.485281374

Reorder the terms:
-9 + x = 8.485281374

Solving
-9 + x = 8.485281374

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = 8.485281374 + 9

Combine like terms: -9 + 9 = 0
0 + x = 8.485281374 + 9
x = 8.485281374 + 9

Combine like terms: 8.485281374 + 9 = 17.485281374
x = 17.485281374

Simplifying
x = 17.485281374

Subproblem 2
x + -9 = -8.485281374

Simplifying
x + -9 = -8.485281374

Reorder the terms:
-9 + x = -8.485281374

Solving
-9 + x = -8.485281374

Solving for variable 'x'.

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

Add '9' to each side of the equation.
-9 + 9 + x = -8.485281374 + 9

Combine like terms: -9 + 9 = 0
0 + x = -8.485281374 + 9
x = -8.485281374 + 9

Combine like terms: -8.485281374 + 9 = 0.514718626
x = 0.514718626

Simplifying
x = 0.514718626

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {17.485281374, 0.514718626}
Solution
x = {17.485281374, 0.514718626}