(6x+3)(x-30)=63-(x+3)

Solution for (6x+3)(x-30)=63-(x+3) equation:

Simplifying
(6x + 3)(x + -30) = 63 + -1(x + 3)

Reorder the terms:
(3 + 6x)(x + -30) = 63 + -1(x + 3)

Reorder the terms:
(3 + 6x)(-30 + x) = 63 + -1(x + 3)

Multiply (3 + 6x) * (-30 + x)
(3(-30 + x) + 6x * (-30 + x)) = 63 + -1(x + 3)
((-30 * 3 + x * 3) + 6x * (-30 + x)) = 63 + -1(x + 3)
((-90 + 3x) + 6x * (-30 + x)) = 63 + -1(x + 3)
(-90 + 3x + (-30 * 6x + x * 6x)) = 63 + -1(x + 3)
(-90 + 3x + (-180x + 6x2)) = 63 + -1(x + 3)

Combine like terms: 3x + -180x = -177x
(-90 + -177x + 6x2) = 63 + -1(x + 3)

Reorder the terms:
-90 + -177x + 6x2 = 63 + -1(3 + x)
-90 + -177x + 6x2 = 63 + (3 * -1 + x * -1)
-90 + -177x + 6x2 = 63 + (-3 + -1x)

Combine like terms: 63 + -3 = 60
-90 + -177x + 6x2 = 60 + -1x

Solving
-90 + -177x + 6x2 = 60 + -1x

Solving for variable 'x'.

Reorder the terms:
-90 + -60 + -177x + x + 6x2 = 60 + -1x + -60 + x

Combine like terms: -90 + -60 = -150
-150 + -177x + x + 6x2 = 60 + -1x + -60 + x

Combine like terms: -177x + x = -176x
-150 + -176x + 6x2 = 60 + -1x + -60 + x

Reorder the terms:
-150 + -176x + 6x2 = 60 + -60 + -1x + x

Combine like terms: 60 + -60 = 0
-150 + -176x + 6x2 = 0 + -1x + x
-150 + -176x + 6x2 = -1x + x

Combine like terms: -1x + x = 0
-150 + -176x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-75 + -88x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-75 + -88x + 3x2)' equal to zero and attempt to solve:

Simplifying
-75 + -88x + 3x2 = 0

Solving
-75 + -88x + 3x2 = 0

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

Divide each side by '3'.
-25 + -29.33333333x + x2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + -29.33333333x + 25 + x2 = 0 + 25

Reorder the terms:
-25 + 25 + -29.33333333x + x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -29.33333333x + x2 = 0 + 25
-29.33333333x + x2 = 0 + 25

Combine like terms: 0 + 25 = 25
-29.33333333x + x2 = 25

The x term is -29.33333333x.  Take half its coefficient (-14.66666667).
Square it (215.1111112) and add it to both sides.

Add '215.1111112' to each side of the equation.
-29.33333333x + 215.1111112 + x2 = 25 + 215.1111112

Reorder the terms:
215.1111112 + -29.33333333x + x2 = 25 + 215.1111112

Combine like terms: 25 + 215.1111112 = 240.1111112
215.1111112 + -29.33333333x + x2 = 240.1111112

Factor a perfect square on the left side:
(x + -14.66666667)(x + -14.66666667) = 240.1111112

Calculate the square root of the right side: 15.495519068

Break this problem into two subproblems by setting 
(x + -14.66666667) equal to 15.495519068 and -15.495519068.

Subproblem 1
x + -14.66666667 = 15.495519068

Simplifying
x + -14.66666667 = 15.495519068

Reorder the terms:
-14.66666667 + x = 15.495519068

Solving
-14.66666667 + x = 15.495519068

Solving for variable 'x'.

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

Add '14.66666667' to each side of the equation.
-14.66666667 + 14.66666667 + x = 15.495519068 + 14.66666667

Combine like terms: -14.66666667 + 14.66666667 = 0.00000000
0.00000000 + x = 15.495519068 + 14.66666667
x = 15.495519068 + 14.66666667

Combine like terms: 15.495519068 + 14.66666667 = 30.162185738
x = 30.162185738

Simplifying
x = 30.162185738

Subproblem 2
x + -14.66666667 = -15.495519068

Simplifying
x + -14.66666667 = -15.495519068

Reorder the terms:
-14.66666667 + x = -15.495519068

Solving
-14.66666667 + x = -15.495519068

Solving for variable 'x'.

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

Add '14.66666667' to each side of the equation.
-14.66666667 + 14.66666667 + x = -15.495519068 + 14.66666667

Combine like terms: -14.66666667 + 14.66666667 = 0.00000000
0.00000000 + x = -15.495519068 + 14.66666667
x = -15.495519068 + 14.66666667

Combine like terms: -15.495519068 + 14.66666667 = -0.828852398
x = -0.828852398

Simplifying
x = -0.828852398

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {30.162185738, -0.828852398}
Solution
x = {30.162185738, -0.828852398}