2x^2+4x-21=24-9x

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Solution for 2x^2+4x-21=24-9x equation: 


Simplifying
2x2 + 4x + -21 = 24 + -9x

Reorder the terms:
-21 + 4x + 2x2 = 24 + -9x

Solving
-21 + 4x + 2x2 = 24 + -9x

Solving for variable 'x'.

Reorder the terms:
-21 + -24 + 4x + 9x + 2x2 = 24 + -9x + -24 + 9x

Combine like terms: -21 + -24 = -45
-45 + 4x + 9x + 2x2 = 24 + -9x + -24 + 9x

Combine like terms: 4x + 9x = 13x
-45 + 13x + 2x2 = 24 + -9x + -24 + 9x

Reorder the terms:
-45 + 13x + 2x2 = 24 + -24 + -9x + 9x

Combine like terms: 24 + -24 = 0
-45 + 13x + 2x2 = 0 + -9x + 9x
-45 + 13x + 2x2 = -9x + 9x

Combine like terms: -9x + 9x = 0
-45 + 13x + 2x2 = 0

Factor a trinomial.
(-9 + -1x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-9, 2.5}

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