0=9x^2-21x-60

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Solution for 0=9x^2-21x-60 equation: 


Simplifying
0 = 9x2 + -21x + -60

Reorder the terms:
0 = -60 + -21x + 9x2

Solving
0 = -60 + -21x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + 60 = 60
60 + 21x + -9x2 = -60 + -21x + 9x2 + 60 + 21x + -9x2

Reorder the terms:
60 + 21x + -9x2 = -60 + 60 + -21x + 21x + 9x2 + -9x2

Combine like terms: -60 + 60 = 0
60 + 21x + -9x2 = 0 + -21x + 21x + 9x2 + -9x2
60 + 21x + -9x2 = -21x + 21x + 9x2 + -9x2

Combine like terms: -21x + 21x = 0
60 + 21x + -9x2 = 0 + 9x2 + -9x2
60 + 21x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
60 + 21x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + 7x + -3x2) = 0

Factor a trinomial.
3((4 + -1x)(5 + 3x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
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
Solution
x = {4, -1.666666667}

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