2x^2+64x+1024=25600

Solution for 2x^2+64x+1024=25600 equation:

Simplifying
2x2 + 64x + 1024 = 25600

Reorder the terms:
1024 + 64x + 2x2 = 25600

Solving
1024 + 64x + 2x2 = 25600

Solving for variable 'x'.

Reorder the terms:
1024 + -25600 + 64x + 2x2 = 25600 + -25600

Combine like terms: 1024 + -25600 = -24576
-24576 + 64x + 2x2 = 25600 + -25600

Combine like terms: 25600 + -25600 = 0
-24576 + 64x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12288 + 32x + x2) = 0

Factor a trinomial.
2((-128 + -1x)(96 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-128 + -1x)' equal to zero and attempt to solve:

Simplifying
-128 + -1x = 0

Solving
-128 + -1x = 0

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

Add '128' to each side of the equation.
-128 + 128 + -1x = 0 + 128

Combine like terms: -128 + 128 = 0
0 + -1x = 0 + 128
-1x = 0 + 128

Combine like terms: 0 + 128 = 128
-1x = 128

Divide each side by '-1'.
x = -128

Simplifying
x = -128
Subproblem 2
Set the factor '(96 + -1x)' equal to zero and attempt to solve:

Simplifying
96 + -1x = 0

Solving
96 + -1x = 0

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

Add '-96' to each side of the equation.
96 + -96 + -1x = 0 + -96

Combine like terms: 96 + -96 = 0
0 + -1x = 0 + -96
-1x = 0 + -96

Combine like terms: 0 + -96 = -96
-1x = -96

Divide each side by '-1'.
x = 96

Simplifying
x = 96
Solution
x = {-128, 96}