0=8x^2+44x-24

Solution for 0=8x^2+44x-24 equation:

Simplifying
0 = 8x2 + 44x + -24

Reorder the terms:
0 = -24 + 44x + 8x2

Solving
0 = -24 + 44x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + 24 = 24
24 + -44x + -8x2 = -24 + 44x + 8x2 + 24 + -44x + -8x2

Reorder the terms:
24 + -44x + -8x2 = -24 + 24 + 44x + -44x + 8x2 + -8x2

Combine like terms: -24 + 24 = 0
24 + -44x + -8x2 = 0 + 44x + -44x + 8x2 + -8x2
24 + -44x + -8x2 = 44x + -44x + 8x2 + -8x2

Combine like terms: 44x + -44x = 0
24 + -44x + -8x2 = 0 + 8x2 + -8x2
24 + -44x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
24 + -44x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(6 + -11x + -2x2) = 0

Factor a trinomial.
4((1 + -2x)(6 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve:

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {0.5, -6}