3x+2x(x-1)=9x+4

Solution for 3x+2x(x-1)=9x+4 equation:

Simplifying
3x + 2x(x + -1) = 9x + 4

Reorder the terms:
3x + 2x(-1 + x) = 9x + 4
3x + (-1 * 2x + x * 2x) = 9x + 4
3x + (-2x + 2x2) = 9x + 4

Combine like terms: 3x + -2x = 1x
1x + 2x2 = 9x + 4

Reorder the terms:
1x + 2x2 = 4 + 9x

Solving
1x + 2x2 = 4 + 9x

Solving for variable 'x'.

Reorder the terms:
-4 + 1x + -9x + 2x2 = 4 + 9x + -4 + -9x

Combine like terms: 1x + -9x = -8x
-4 + -8x + 2x2 = 4 + 9x + -4 + -9x

Reorder the terms:
-4 + -8x + 2x2 = 4 + -4 + 9x + -9x

Combine like terms: 4 + -4 = 0
-4 + -8x + 2x2 = 0 + 9x + -9x
-4 + -8x + 2x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-4 + -8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -4x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -4x + x2 = 0

Solving
-2 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -4x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -4x + x2 = 0 + 2
-4x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-4x + x2 = 2

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 2 + 4

Reorder the terms:
4 + -4x + x2 = 2 + 4

Combine like terms: 2 + 4 = 6
4 + -4x + x2 = 6

Factor a perfect square on the left side:
(x + -2)(x + -2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -2) equal to 2.449489743 and -2.449489743.

Subproblem 1
x + -2 = 2.449489743

Simplifying
x + -2 = 2.449489743

Reorder the terms:
-2 + x = 2.449489743

Solving
-2 + x = 2.449489743

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.449489743 + 2
x = 2.449489743 + 2

Combine like terms: 2.449489743 + 2 = 4.449489743
x = 4.449489743

Simplifying
x = 4.449489743

Subproblem 2
x + -2 = -2.449489743

Simplifying
x + -2 = -2.449489743

Reorder the terms:
-2 + x = -2.449489743

Solving
-2 + x = -2.449489743

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.449489743 + 2
x = -2.449489743 + 2

Combine like terms: -2.449489743 + 2 = -0.449489743
x = -0.449489743

Simplifying
x = -0.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.449489743, -0.449489743}
Solution
x = {4.449489743, -0.449489743}