(5x+4)(x-10)=61-(x+1)

Solution for (5x+4)(x-10)=61-(x+1) equation:

Simplifying
(5x + 4)(x + -10) = 61 + -1(x + 1)

Reorder the terms:
(4 + 5x)(x + -10) = 61 + -1(x + 1)

Reorder the terms:
(4 + 5x)(-10 + x) = 61 + -1(x + 1)

Multiply (4 + 5x) * (-10 + x)
(4(-10 + x) + 5x * (-10 + x)) = 61 + -1(x + 1)
((-10 * 4 + x * 4) + 5x * (-10 + x)) = 61 + -1(x + 1)
((-40 + 4x) + 5x * (-10 + x)) = 61 + -1(x + 1)
(-40 + 4x + (-10 * 5x + x * 5x)) = 61 + -1(x + 1)
(-40 + 4x + (-50x + 5x2)) = 61 + -1(x + 1)

Combine like terms: 4x + -50x = -46x
(-40 + -46x + 5x2) = 61 + -1(x + 1)

Reorder the terms:
-40 + -46x + 5x2 = 61 + -1(1 + x)
-40 + -46x + 5x2 = 61 + (1 * -1 + x * -1)
-40 + -46x + 5x2 = 61 + (-1 + -1x)

Combine like terms: 61 + -1 = 60
-40 + -46x + 5x2 = 60 + -1x

Solving
-40 + -46x + 5x2 = 60 + -1x

Solving for variable 'x'.

Reorder the terms:
-40 + -60 + -46x + x + 5x2 = 60 + -1x + -60 + x

Combine like terms: -40 + -60 = -100
-100 + -46x + x + 5x2 = 60 + -1x + -60 + x

Combine like terms: -46x + x = -45x
-100 + -45x + 5x2 = 60 + -1x + -60 + x

Reorder the terms:
-100 + -45x + 5x2 = 60 + -60 + -1x + x

Combine like terms: 60 + -60 = 0
-100 + -45x + 5x2 = 0 + -1x + x
-100 + -45x + 5x2 = -1x + x

Combine like terms: -1x + x = 0
-100 + -45x + 5x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-20 + -9x + x2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-20 + -9x + x2)' equal to zero and attempt to solve:

Simplifying
-20 + -9x + x2 = 0

Solving
-20 + -9x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -9x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -9x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -9x + x2 = 0 + 20
-9x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-9x + x2 = 20

The x term is -9x.  Take half its coefficient (-4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
-9x + 20.25 + x2 = 20 + 20.25

Reorder the terms:
20.25 + -9x + x2 = 20 + 20.25

Combine like terms: 20 + 20.25 = 40.25
20.25 + -9x + x2 = 40.25

Factor a perfect square on the left side:
(x + -4.5)(x + -4.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(x + -4.5) equal to 6.34428877 and -6.34428877.

Subproblem 1
x + -4.5 = 6.34428877

Simplifying
x + -4.5 = 6.34428877

Reorder the terms:
-4.5 + x = 6.34428877

Solving
-4.5 + x = 6.34428877

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = 6.34428877 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = 6.34428877 + 4.5
x = 6.34428877 + 4.5

Combine like terms: 6.34428877 + 4.5 = 10.84428877
x = 10.84428877

Simplifying
x = 10.84428877

Subproblem 2
x + -4.5 = -6.34428877

Simplifying
x + -4.5 = -6.34428877

Reorder the terms:
-4.5 + x = -6.34428877

Solving
-4.5 + x = -6.34428877

Solving for variable 'x'.

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

Add '4.5' to each side of the equation.
-4.5 + 4.5 + x = -6.34428877 + 4.5

Combine like terms: -4.5 + 4.5 = 0.0
0.0 + x = -6.34428877 + 4.5
x = -6.34428877 + 4.5

Combine like terms: -6.34428877 + 4.5 = -1.84428877
x = -1.84428877

Simplifying
x = -1.84428877

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.84428877, -1.84428877}
Solution
x = {10.84428877, -1.84428877}