10(x+3)(-9x-4)=x-5+3

Solution for 10(x+3)(-9x-4)=x-5+3 equation:

Simplifying
10(x + 3)(-9x + -4) = x + -5 + 3

Reorder the terms:
10(3 + x)(-9x + -4) = x + -5 + 3

Reorder the terms:
10(3 + x)(-4 + -9x) = x + -5 + 3

Multiply (3 + x) * (-4 + -9x)
10(3(-4 + -9x) + x(-4 + -9x)) = x + -5 + 3
10((-4 * 3 + -9x * 3) + x(-4 + -9x)) = x + -5 + 3
10((-12 + -27x) + x(-4 + -9x)) = x + -5 + 3
10(-12 + -27x + (-4 * x + -9x * x)) = x + -5 + 3
10(-12 + -27x + (-4x + -9x2)) = x + -5 + 3

Combine like terms: -27x + -4x = -31x
10(-12 + -31x + -9x2) = x + -5 + 3
(-12 * 10 + -31x * 10 + -9x2 * 10) = x + -5 + 3
(-120 + -310x + -90x2) = x + -5 + 3

Reorder the terms:
-120 + -310x + -90x2 = -5 + 3 + x

Combine like terms: -5 + 3 = -2
-120 + -310x + -90x2 = -2 + x

Solving
-120 + -310x + -90x2 = -2 + x

Solving for variable 'x'.

Reorder the terms:
-120 + 2 + -310x + -1x + -90x2 = -2 + x + 2 + -1x

Combine like terms: -120 + 2 = -118
-118 + -310x + -1x + -90x2 = -2 + x + 2 + -1x

Combine like terms: -310x + -1x = -311x
-118 + -311x + -90x2 = -2 + x + 2 + -1x

Reorder the terms:
-118 + -311x + -90x2 = -2 + 2 + x + -1x

Combine like terms: -2 + 2 = 0
-118 + -311x + -90x2 = 0 + x + -1x
-118 + -311x + -90x2 = x + -1x

Combine like terms: x + -1x = 0
-118 + -311x + -90x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(118 + 311x + 90x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(118 + 311x + 90x2)' equal to zero and attempt to solve:

Simplifying
118 + 311x + 90x2 = 0

Solving
118 + 311x + 90x2 = 0

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

Divide each side by '90'.
1.311111111 + 3.455555556x + x2 = 0.0

Move the constant term to the right:

Add '-1.311111111' to each side of the equation.
1.311111111 + 3.455555556x + -1.311111111 + x2 = 0.0 + -1.311111111

Reorder the terms:
1.311111111 + -1.311111111 + 3.455555556x + x2 = 0.0 + -1.311111111

Combine like terms: 1.311111111 + -1.311111111 = 0.000000000
0.000000000 + 3.455555556x + x2 = 0.0 + -1.311111111
3.455555556x + x2 = 0.0 + -1.311111111

Combine like terms: 0.0 + -1.311111111 = -1.311111111
3.455555556x + x2 = -1.311111111

The x term is 3.455555556x.  Take half its coefficient (1.727777778).
Square it (2.985216050) and add it to both sides.

Add '2.985216050' to each side of the equation.
3.455555556x + 2.985216050 + x2 = -1.311111111 + 2.985216050

Reorder the terms:
2.985216050 + 3.455555556x + x2 = -1.311111111 + 2.985216050

Combine like terms: -1.311111111 + 2.985216050 = 1.674104939
2.985216050 + 3.455555556x + x2 = 1.674104939

Factor a perfect square on the left side:
(x + 1.727777778)(x + 1.727777778) = 1.674104939

Calculate the square root of the right side: 1.293872072

Break this problem into two subproblems by setting 
(x + 1.727777778) equal to 1.293872072 and -1.293872072.

Subproblem 1
x + 1.727777778 = 1.293872072

Simplifying
x + 1.727777778 = 1.293872072

Reorder the terms:
1.727777778 + x = 1.293872072

Solving
1.727777778 + x = 1.293872072

Solving for variable 'x'.

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

Add '-1.727777778' to each side of the equation.
1.727777778 + -1.727777778 + x = 1.293872072 + -1.727777778

Combine like terms: 1.727777778 + -1.727777778 = 0.000000000
0.000000000 + x = 1.293872072 + -1.727777778
x = 1.293872072 + -1.727777778

Combine like terms: 1.293872072 + -1.727777778 = -0.433905706
x = -0.433905706

Simplifying
x = -0.433905706

Subproblem 2
x + 1.727777778 = -1.293872072

Simplifying
x + 1.727777778 = -1.293872072

Reorder the terms:
1.727777778 + x = -1.293872072

Solving
1.727777778 + x = -1.293872072

Solving for variable 'x'.

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

Add '-1.727777778' to each side of the equation.
1.727777778 + -1.727777778 + x = -1.293872072 + -1.727777778

Combine like terms: 1.727777778 + -1.727777778 = 0.000000000
0.000000000 + x = -1.293872072 + -1.727777778
x = -1.293872072 + -1.727777778

Combine like terms: -1.293872072 + -1.727777778 = -3.02164985
x = -3.02164985

Simplifying
x = -3.02164985

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.433905706, -3.02164985}
Solution
x = {-0.433905706, -3.02164985}