X^2(2X+1)+9X=X^2(6X+1)

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Solution for X^2(2X+1)+9X=X^2(6X+1) equation: 


Simplifying
X2(2X + 1) + 9X = X2(6X + 1)

Reorder the terms:
X2(1 + 2X) + 9X = X2(6X + 1)
(1 * X2 + 2X * X2) + 9X = X2(6X + 1)
(1X2 + 2X3) + 9X = X2(6X + 1)

Reorder the terms:
9X + 1X2 + 2X3 = X2(6X + 1)

Reorder the terms:
9X + 1X2 + 2X3 = X2(1 + 6X)
9X + 1X2 + 2X3 = (1 * X2 + 6X * X2)
9X + 1X2 + 2X3 = (1X2 + 6X3)

Add '-1X2' to each side of the equation.
9X + 1X2 + -1X2 + 2X3 = 1X2 + -1X2 + 6X3

Combine like terms: 1X2 + -1X2 = 0
9X + 0 + 2X3 = 1X2 + -1X2 + 6X3
9X + 2X3 = 1X2 + -1X2 + 6X3

Combine like terms: 1X2 + -1X2 = 0
9X + 2X3 = 0 + 6X3
9X + 2X3 = 6X3

Solving
9X + 2X3 = 6X3

Solving for variable 'X'.

Combine like terms: 2X3 + -6X3 = -4X3
9X + -4X3 = 6X3 + -6X3

Combine like terms: 6X3 + -6X3 = 0
9X + -4X3 = 0

Factor out the Greatest Common Factor (GCF), 'X'.
X(9 + -4X2) = 0

Factor a difference between two squares.
X((3 + 2X)(3 + -2X)) = 0


Subproblem 1
Set the factor 'X' equal to zero and attempt to solve:

Simplifying
X = 0

Solving
X = 0

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

Simplifying
X = 0

Subproblem 2
Set the factor '(3 + 2X)' equal to zero and attempt to solve:

Simplifying
3 + 2X = 0

Solving
3 + 2X = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2X = 0 + -3
2X = 0 + -3

Combine like terms: 0 + -3 = -3
2X = -3

Divide each side by '2'.
X = -1.5

Simplifying
X = -1.5

Subproblem 3
Set the factor '(3 + -2X)' equal to zero and attempt to solve:

Simplifying
3 + -2X = 0

Solving
3 + -2X = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2X = 0 + -3
-2X = 0 + -3

Combine like terms: 0 + -3 = -3
-2X = -3

Divide each side by '-2'.
X = 1.5

Simplifying
X = 1.5
Solution
X = {0, -1.5, 1.5}

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