5(x-4)+8(2x+2)=6(x+1)5(x+10)

Solution for 5(x-4)+8(2x+2)=6(x+1)5(x+10) equation:

Simplifying
5(x + -4) + 8(2x + 2) = 6(x + 1) * 5(x + 10)

Reorder the terms:
5(-4 + x) + 8(2x + 2) = 6(x + 1) * 5(x + 10)
(-4 * 5 + x * 5) + 8(2x + 2) = 6(x + 1) * 5(x + 10)
(-20 + 5x) + 8(2x + 2) = 6(x + 1) * 5(x + 10)

Reorder the terms:
-20 + 5x + 8(2 + 2x) = 6(x + 1) * 5(x + 10)
-20 + 5x + (2 * 8 + 2x * 8) = 6(x + 1) * 5(x + 10)
-20 + 5x + (16 + 16x) = 6(x + 1) * 5(x + 10)

Reorder the terms:
-20 + 16 + 5x + 16x = 6(x + 1) * 5(x + 10)

Combine like terms: -20 + 16 = -4
-4 + 5x + 16x = 6(x + 1) * 5(x + 10)

Combine like terms: 5x + 16x = 21x
-4 + 21x = 6(x + 1) * 5(x + 10)

Reorder the terms:
-4 + 21x = 6(1 + x) * 5(x + 10)

Reorder the terms:
-4 + 21x = 6(1 + x) * 5(10 + x)

Reorder the terms for easier multiplication:
-4 + 21x = 6 * 5(1 + x)(10 + x)

Multiply 6 * 5
-4 + 21x = 30(1 + x)(10 + x)

Multiply (1 + x) * (10 + x)
-4 + 21x = 30(1(10 + x) + x(10 + x))
-4 + 21x = 30((10 * 1 + x * 1) + x(10 + x))
-4 + 21x = 30((10 + 1x) + x(10 + x))
-4 + 21x = 30(10 + 1x + (10 * x + x * x))
-4 + 21x = 30(10 + 1x + (10x + x2))

Combine like terms: 1x + 10x = 11x
-4 + 21x = 30(10 + 11x + x2)
-4 + 21x = (10 * 30 + 11x * 30 + x2 * 30)
-4 + 21x = (300 + 330x + 30x2)

Solving
-4 + 21x = 300 + 330x + 30x2

Solving for variable 'x'.

Reorder the terms:
-4 + -300 + 21x + -330x + -30x2 = 300 + 330x + 30x2 + -300 + -330x + -30x2

Combine like terms: -4 + -300 = -304
-304 + 21x + -330x + -30x2 = 300 + 330x + 30x2 + -300 + -330x + -30x2

Combine like terms: 21x + -330x = -309x
-304 + -309x + -30x2 = 300 + 330x + 30x2 + -300 + -330x + -30x2

Reorder the terms:
-304 + -309x + -30x2 = 300 + -300 + 330x + -330x + 30x2 + -30x2

Combine like terms: 300 + -300 = 0
-304 + -309x + -30x2 = 0 + 330x + -330x + 30x2 + -30x2
-304 + -309x + -30x2 = 330x + -330x + 30x2 + -30x2

Combine like terms: 330x + -330x = 0
-304 + -309x + -30x2 = 0 + 30x2 + -30x2
-304 + -309x + -30x2 = 30x2 + -30x2

Combine like terms: 30x2 + -30x2 = 0
-304 + -309x + -30x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(304 + 309x + 30x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(304 + 309x + 30x2)' equal to zero and attempt to solve:

Simplifying
304 + 309x + 30x2 = 0

Solving
304 + 309x + 30x2 = 0

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

Divide each side by '30'.
10.13333333 + 10.3x + x2 = 0.0

Move the constant term to the right:

Add '-10.13333333' to each side of the equation.
10.13333333 + 10.3x + -10.13333333 + x2 = 0.0 + -10.13333333

Reorder the terms:
10.13333333 + -10.13333333 + 10.3x + x2 = 0.0 + -10.13333333

Combine like terms: 10.13333333 + -10.13333333 = 0.00000000
0.00000000 + 10.3x + x2 = 0.0 + -10.13333333
10.3x + x2 = 0.0 + -10.13333333

Combine like terms: 0.0 + -10.13333333 = -10.13333333
10.3x + x2 = -10.13333333

The x term is 10.3x.  Take half its coefficient (5.15).
Square it (26.5225) and add it to both sides.

Add '26.5225' to each side of the equation.
10.3x + 26.5225 + x2 = -10.13333333 + 26.5225

Reorder the terms:
26.5225 + 10.3x + x2 = -10.13333333 + 26.5225

Combine like terms: -10.13333333 + 26.5225 = 16.38916667
26.5225 + 10.3x + x2 = 16.38916667

Factor a perfect square on the left side:
(x + 5.15)(x + 5.15) = 16.38916667

Calculate the square root of the right side: 4.048353575

Break this problem into two subproblems by setting 
(x + 5.15) equal to 4.048353575 and -4.048353575.

Subproblem 1
x + 5.15 = 4.048353575

Simplifying
x + 5.15 = 4.048353575

Reorder the terms:
5.15 + x = 4.048353575

Solving
5.15 + x = 4.048353575

Solving for variable 'x'.

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

Add '-5.15' to each side of the equation.
5.15 + -5.15 + x = 4.048353575 + -5.15

Combine like terms: 5.15 + -5.15 = 0.00
0.00 + x = 4.048353575 + -5.15
x = 4.048353575 + -5.15

Combine like terms: 4.048353575 + -5.15 = -1.101646425
x = -1.101646425

Simplifying
x = -1.101646425

Subproblem 2
x + 5.15 = -4.048353575

Simplifying
x + 5.15 = -4.048353575

Reorder the terms:
5.15 + x = -4.048353575

Solving
5.15 + x = -4.048353575

Solving for variable 'x'.

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

Add '-5.15' to each side of the equation.
5.15 + -5.15 + x = -4.048353575 + -5.15

Combine like terms: 5.15 + -5.15 = 0.00
0.00 + x = -4.048353575 + -5.15
x = -4.048353575 + -5.15

Combine like terms: -4.048353575 + -5.15 = -9.198353575
x = -9.198353575

Simplifying
x = -9.198353575

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.101646425, -9.198353575}
Solution
x = {-1.101646425, -9.198353575}