8x^2-24x=14

Solution for 8x^2-24x=14 equation:

Simplifying
8x2 + -24x = 14

Reorder the terms:
-24x + 8x2 = 14

Solving
-24x + 8x2 = 14

Solving for variable 'x'.

Reorder the terms:
-14 + -24x + 8x2 = 14 + -14

Combine like terms: 14 + -14 = 0
-14 + -24x + 8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -12x + 4x2) = 0

Factor a trinomial.
2((-1 + -2x)(7 + -2x)) = 0

Ignore the factor 2.
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 '(7 + -2x)' equal to zero and attempt to solve:

Simplifying
7 + -2x = 0

Solving
7 + -2x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2x = 0 + -7
-2x = 0 + -7

Combine like terms: 0 + -7 = -7
-2x = -7

Divide each side by '-2'.
x = 3.5

Simplifying
x = 3.5
Solution
x = {-0.5, 3.5}