X^2(2X+5)=21X+X^2(X+9)

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Solution for X^2(2X+5)=21X+X^2(X+9) equation: 


Simplifying
X2(2X + 5) = 21X + X2(X + 9)

Reorder the terms:
X2(5 + 2X) = 21X + X2(X + 9)
(5 * X2 + 2X * X2) = 21X + X2(X + 9)
(5X2 + 2X3) = 21X + X2(X + 9)

Reorder the terms:
5X2 + 2X3 = 21X + X2(9 + X)
5X2 + 2X3 = 21X + (9 * X2 + X * X2)
5X2 + 2X3 = 21X + (9X2 + X3)

Solving
5X2 + 2X3 = 21X + 9X2 + X3

Solving for variable 'X'.

Reorder the terms:
-21X + 5X2 + -9X2 + 2X3 + -1X3 = 21X + 9X2 + X3 + -21X + -9X2 + -1X3

Combine like terms: 5X2 + -9X2 = -4X2
-21X + -4X2 + 2X3 + -1X3 = 21X + 9X2 + X3 + -21X + -9X2 + -1X3

Combine like terms: 2X3 + -1X3 = 1X3
-21X + -4X2 + 1X3 = 21X + 9X2 + X3 + -21X + -9X2 + -1X3

Reorder the terms:
-21X + -4X2 + 1X3 = 21X + -21X + 9X2 + -9X2 + X3 + -1X3

Combine like terms: 21X + -21X = 0
-21X + -4X2 + 1X3 = 0 + 9X2 + -9X2 + X3 + -1X3
-21X + -4X2 + 1X3 = 9X2 + -9X2 + X3 + -1X3

Combine like terms: 9X2 + -9X2 = 0
-21X + -4X2 + 1X3 = 0 + X3 + -1X3
-21X + -4X2 + 1X3 = X3 + -1X3

Combine like terms: X3 + -1X3 = 0
-21X + -4X2 + 1X3 = 0

Factor out the Greatest Common Factor (GCF), 'X'.
X(-21 + -4X + X2) = 0

Factor a trinomial.
X((-3 + -1X)(7 + -1X)) = 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 + -1X)' equal to zero and attempt to solve:

Simplifying
-3 + -1X = 0

Solving
-3 + -1X = 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 + -1X = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1X = 0 + 3
-1X = 0 + 3

Combine like terms: 0 + 3 = 3
-1X = 3

Divide each side by '-1'.
X = -3

Simplifying
X = -3

Subproblem 3
Set the factor '(7 + -1X)' equal to zero and attempt to solve:

Simplifying
7 + -1X = 0

Solving
7 + -1X = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1X = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1X = 0 + -7
-1X = 0 + -7

Combine like terms: 0 + -7 = -7
-1X = -7

Divide each side by '-1'.
X = 7

Simplifying
X = 7
Solution
X = {0, -3, 7}

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