1588=2x^2+24x+308

Solution for 1588=2x^2+24x+308 equation:

Simplifying
1588 = 2x2 + 24x + 308

Reorder the terms:
1588 = 308 + 24x + 2x2

Solving
1588 = 308 + 24x + 2x2

Solving for variable 'x'.

Combine like terms: 1588 + -308 = 1280
1280 + -24x + -2x2 = 308 + 24x + 2x2 + -308 + -24x + -2x2

Reorder the terms:
1280 + -24x + -2x2 = 308 + -308 + 24x + -24x + 2x2 + -2x2

Combine like terms: 308 + -308 = 0
1280 + -24x + -2x2 = 0 + 24x + -24x + 2x2 + -2x2
1280 + -24x + -2x2 = 24x + -24x + 2x2 + -2x2

Combine like terms: 24x + -24x = 0
1280 + -24x + -2x2 = 0 + 2x2 + -2x2
1280 + -24x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1280 + -24x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(640 + -12x + -1x2) = 0

Factor a trinomial.
2((20 + -1x)(32 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Subproblem 2
Set the factor '(32 + x)' equal to zero and attempt to solve:

Simplifying
32 + x = 0

Solving
32 + x = 0

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

Add '-32' to each side of the equation.
32 + -32 + x = 0 + -32

Combine like terms: 32 + -32 = 0
0 + x = 0 + -32
x = 0 + -32

Combine like terms: 0 + -32 = -32
x = -32

Simplifying
x = -32
Solution
x = {20, -32}