9x^2+13x=-6x+24

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Solution for 9x^2+13x=-6x+24 equation: 


Simplifying
9x2 + 13x = -6x + 24

Reorder the terms:
13x + 9x2 = -6x + 24

Reorder the terms:
13x + 9x2 = 24 + -6x

Solving
13x + 9x2 = 24 + -6x

Solving for variable 'x'.

Reorder the terms:
-24 + 13x + 6x + 9x2 = 24 + -6x + -24 + 6x

Combine like terms: 13x + 6x = 19x
-24 + 19x + 9x2 = 24 + -6x + -24 + 6x

Reorder the terms:
-24 + 19x + 9x2 = 24 + -24 + -6x + 6x

Combine like terms: 24 + -24 = 0
-24 + 19x + 9x2 = 0 + -6x + 6x
-24 + 19x + 9x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
-24 + 19x + 9x2 = 0

Factor a trinomial.
(-3 + -1x)(8 + -9x) = 0


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 '(8 + -9x)' equal to zero and attempt to solve:

Simplifying
8 + -9x = 0

Solving
8 + -9x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -9x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -9x = 0 + -8
-9x = 0 + -8

Combine like terms: 0 + -8 = -8
-9x = -8

Divide each side by '-9'.
x = 0.8888888889

Simplifying
x = 0.8888888889
Solution
x = {-3, 0.8888888889}

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