(6x+3)(x-10)=61-(x+1)

Solution for (6x+3)(x-10)=61-(x+1) equation:

Simplifying
(6x + 3)(x + -10) = 61 + -1(x + 1)

Reorder the terms:
(3 + 6x)(x + -10) = 61 + -1(x + 1)

Reorder the terms:
(3 + 6x)(-10 + x) = 61 + -1(x + 1)

Multiply (3 + 6x) * (-10 + x)
(3(-10 + x) + 6x * (-10 + x)) = 61 + -1(x + 1)
((-10 * 3 + x * 3) + 6x * (-10 + x)) = 61 + -1(x + 1)
((-30 + 3x) + 6x * (-10 + x)) = 61 + -1(x + 1)
(-30 + 3x + (-10 * 6x + x * 6x)) = 61 + -1(x + 1)
(-30 + 3x + (-60x + 6x2)) = 61 + -1(x + 1)

Combine like terms: 3x + -60x = -57x
(-30 + -57x + 6x2) = 61 + -1(x + 1)

Reorder the terms:
-30 + -57x + 6x2 = 61 + -1(1 + x)
-30 + -57x + 6x2 = 61 + (1 * -1 + x * -1)
-30 + -57x + 6x2 = 61 + (-1 + -1x)

Combine like terms: 61 + -1 = 60
-30 + -57x + 6x2 = 60 + -1x

Solving
-30 + -57x + 6x2 = 60 + -1x

Solving for variable 'x'.

Reorder the terms:
-30 + -60 + -57x + x + 6x2 = 60 + -1x + -60 + x

Combine like terms: -30 + -60 = -90
-90 + -57x + x + 6x2 = 60 + -1x + -60 + x

Combine like terms: -57x + x = -56x
-90 + -56x + 6x2 = 60 + -1x + -60 + x

Reorder the terms:
-90 + -56x + 6x2 = 60 + -60 + -1x + x

Combine like terms: 60 + -60 = 0
-90 + -56x + 6x2 = 0 + -1x + x
-90 + -56x + 6x2 = -1x + x

Combine like terms: -1x + x = 0
-90 + -56x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-45 + -28x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-45 + -28x + 3x2)' equal to zero and attempt to solve:

Simplifying
-45 + -28x + 3x2 = 0

Solving
-45 + -28x + 3x2 = 0

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

Divide each side by '3'.
-15 + -9.333333333x + x2 = 0

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + -9.333333333x + 15 + x2 = 0 + 15

Reorder the terms:
-15 + 15 + -9.333333333x + x2 = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -9.333333333x + x2 = 0 + 15
-9.333333333x + x2 = 0 + 15

Combine like terms: 0 + 15 = 15
-9.333333333x + x2 = 15

The x term is -9.333333333x.  Take half its coefficient (-4.666666667).
Square it (21.77777778) and add it to both sides.

Add '21.77777778' to each side of the equation.
-9.333333333x + 21.77777778 + x2 = 15 + 21.77777778

Reorder the terms:
21.77777778 + -9.333333333x + x2 = 15 + 21.77777778

Combine like terms: 15 + 21.77777778 = 36.77777778
21.77777778 + -9.333333333x + x2 = 36.77777778

Factor a perfect square on the left side:
(x + -4.666666667)(x + -4.666666667) = 36.77777778

Calculate the square root of the right side: 6.064468466

Break this problem into two subproblems by setting 
(x + -4.666666667) equal to 6.064468466 and -6.064468466.

Subproblem 1
x + -4.666666667 = 6.064468466

Simplifying
x + -4.666666667 = 6.064468466

Reorder the terms:
-4.666666667 + x = 6.064468466

Solving
-4.666666667 + x = 6.064468466

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = 6.064468466 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = 6.064468466 + 4.666666667
x = 6.064468466 + 4.666666667

Combine like terms: 6.064468466 + 4.666666667 = 10.731135133
x = 10.731135133

Simplifying
x = 10.731135133

Subproblem 2
x + -4.666666667 = -6.064468466

Simplifying
x + -4.666666667 = -6.064468466

Reorder the terms:
-4.666666667 + x = -6.064468466

Solving
-4.666666667 + x = -6.064468466

Solving for variable 'x'.

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

Add '4.666666667' to each side of the equation.
-4.666666667 + 4.666666667 + x = -6.064468466 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + x = -6.064468466 + 4.666666667
x = -6.064468466 + 4.666666667

Combine like terms: -6.064468466 + 4.666666667 = -1.397801799
x = -1.397801799

Simplifying
x = -1.397801799

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.731135133, -1.397801799}
Solution
x = {10.731135133, -1.397801799}