0=3x^2+4x-6-9

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Solution for 0=3x^2+4x-6-9 equation: 


Simplifying
0 = 3x2 + 4x + -6 + -9

Reorder the terms:
0 = -6 + -9 + 4x + 3x2

Combine like terms: -6 + -9 = -15
0 = -15 + 4x + 3x2

Solving
0 = -15 + 4x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + 15 = 15
15 + -4x + -3x2 = -15 + 4x + 3x2 + 15 + -4x + -3x2

Reorder the terms:
15 + -4x + -3x2 = -15 + 15 + 4x + -4x + 3x2 + -3x2

Combine like terms: -15 + 15 = 0
15 + -4x + -3x2 = 0 + 4x + -4x + 3x2 + -3x2
15 + -4x + -3x2 = 4x + -4x + 3x2 + -3x2

Combine like terms: 4x + -4x = 0
15 + -4x + -3x2 = 0 + 3x2 + -3x2
15 + -4x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
15 + -4x + -3x2 = 0

Factor a trinomial.
(5 + -3x)(3 + x) = 0


Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {1.666666667, -3}

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