2x^2+40x=-102

Solution for 2x^2+40x=-102 equation:

Simplifying
2x2 + 40x = -102

Reorder the terms:
40x + 2x2 = -102

Solving
40x + 2x2 = -102

Solving for variable 'x'.

Reorder the terms:
102 + 40x + 2x2 = -102 + 102

Combine like terms: -102 + 102 = 0
102 + 40x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(51 + 20x + x2) = 0

Factor a trinomial.
2((17 + x)(3 + x)) = 0

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

Simplifying
17 + x = 0

Solving
17 + x = 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 + x = 0 + -17

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

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

Simplifying
x = -17
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-17, -3}