3x^2+22=9x^2+24x+22

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Solution for 3x^2+22=9x^2+24x+22 equation: 


Simplifying
3x2 + 22 = 9x2 + 24x + 22

Reorder the terms:
22 + 3x2 = 9x2 + 24x + 22

Reorder the terms:
22 + 3x2 = 22 + 24x + 9x2

Add '-22' to each side of the equation.
22 + -22 + 3x2 = 22 + 24x + -22 + 9x2

Combine like terms: 22 + -22 = 0
0 + 3x2 = 22 + 24x + -22 + 9x2
3x2 = 22 + 24x + -22 + 9x2

Reorder the terms:
3x2 = 22 + -22 + 24x + 9x2

Combine like terms: 22 + -22 = 0
3x2 = 0 + 24x + 9x2
3x2 = 24x + 9x2

Solving
3x2 = 24x + 9x2

Solving for variable 'x'.

Reorder the terms:
-24x + 3x2 + -9x2 = 24x + 9x2 + -24x + -9x2

Combine like terms: 3x2 + -9x2 = -6x2
-24x + -6x2 = 24x + 9x2 + -24x + -9x2

Reorder the terms:
-24x + -6x2 = 24x + -24x + 9x2 + -9x2

Combine like terms: 24x + -24x = 0
-24x + -6x2 = 0 + 9x2 + -9x2
-24x + -6x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-24x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '-6x'.
-6x(4 + x) = 0

Ignore the factor -6.

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 '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

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

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

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

Simplifying
x = -4
Solution
x = {0, -4}

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