2x^2+32x+256=290

Solution for 2x^2+32x+256=290 equation:

Simplifying
2x2 + 32x + 256 = 290

Reorder the terms:
256 + 32x + 2x2 = 290

Solving
256 + 32x + 2x2 = 290

Solving for variable 'x'.

Reorder the terms:
256 + -290 + 32x + 2x2 = 290 + -290

Combine like terms: 256 + -290 = -34
-34 + 32x + 2x2 = 290 + -290

Combine like terms: 290 + -290 = 0
-34 + 32x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 16x + x2) = 0

Factor a trinomial.
2((-17 + -1x)(1 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-17 + -1x)' equal to zero and attempt to solve:

Simplifying
-17 + -1x = 0

Solving
-17 + -1x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1x = 0 + 17
-1x = 0 + 17

Combine like terms: 0 + 17 = 17
-1x = 17

Divide each side by '-1'.
x = -17

Simplifying
x = -17
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Solution
x = {-17, 1}