2x^2+24x+8=64

Solution for 2x^2+24x+8=64 equation:

Simplifying
2x2 + 24x + 8 = 64

Reorder the terms:
8 + 24x + 2x2 = 64

Solving
8 + 24x + 2x2 = 64

Solving for variable 'x'.

Reorder the terms:
8 + -64 + 24x + 2x2 = 64 + -64

Combine like terms: 8 + -64 = -56
-56 + 24x + 2x2 = 64 + -64

Combine like terms: 64 + -64 = 0
-56 + 24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + 12x + x2) = 0

Factor a trinomial.
2((-14 + -1x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + -1x)' equal to zero and attempt to solve:

Simplifying
-14 + -1x = 0

Solving
-14 + -1x = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1x = 0 + 14
-1x = 0 + 14

Combine like terms: 0 + 14 = 14
-1x = 14

Divide each side by '-1'.
x = -14

Simplifying
x = -14
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-14, 2}