6x^2+21x=18+9x

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Solution for 6x^2+21x=18+9x equation: 


Simplifying
6x2 + 21x = 18 + 9x

Reorder the terms:
21x + 6x2 = 18 + 9x

Solving
21x + 6x2 = 18 + 9x

Solving for variable 'x'.

Reorder the terms:
-18 + 21x + -9x + 6x2 = 18 + 9x + -18 + -9x

Combine like terms: 21x + -9x = 12x
-18 + 12x + 6x2 = 18 + 9x + -18 + -9x

Reorder the terms:
-18 + 12x + 6x2 = 18 + -18 + 9x + -9x

Combine like terms: 18 + -18 = 0
-18 + 12x + 6x2 = 0 + 9x + -9x
-18 + 12x + 6x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-18 + 12x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-3 + 2x + x2) = 0

Factor a trinomial.
6((-3 + -1x)(1 + -1x)) = 0

Ignore the factor 6.

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-3, 1}

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