0=24x^2-21x-3

Solution for 0=24x^2-21x-3 equation:

Simplifying
0 = 24x2 + -21x + -3

Reorder the terms:
0 = -3 + -21x + 24x2

Solving
0 = -3 + -21x + 24x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + 21x + -24x2 = -3 + -21x + 24x2 + 3 + 21x + -24x2

Reorder the terms:
3 + 21x + -24x2 = -3 + 3 + -21x + 21x + 24x2 + -24x2

Combine like terms: -3 + 3 = 0
3 + 21x + -24x2 = 0 + -21x + 21x + 24x2 + -24x2
3 + 21x + -24x2 = -21x + 21x + 24x2 + -24x2

Combine like terms: -21x + 21x = 0
3 + 21x + -24x2 = 0 + 24x2 + -24x2
3 + 21x + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
3 + 21x + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + 7x + -8x2) = 0

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

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + 8x)' equal to zero and attempt to solve:

Simplifying
1 + 8x = 0

Solving
1 + 8x = 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 + 8x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8x = 0 + -1
8x = 0 + -1

Combine like terms: 0 + -1 = -1
8x = -1

Divide each side by '8'.
x = -0.125

Simplifying
x = -0.125
Solution
x = {1, -0.125}