2x^2+25x+75=0

Solution for 2x^2+25x+75=0 equation:

Simplifying
2x2 + 25x + 75 = 0

Reorder the terms:
75 + 25x + 2x2 = 0

Solving
75 + 25x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(15 + 2x)(5 + x) = 0

Subproblem 1
Set the factor '(15 + 2x)' equal to zero and attempt to solve:

Simplifying
15 + 2x = 0

Solving
15 + 2x = 0

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

Add '-15' to each side of the equation.
15 + -15 + 2x = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 2x = 0 + -15
2x = 0 + -15

Combine like terms: 0 + -15 = -15
2x = -15

Divide each side by '2'.
x = -7.5

Simplifying
x = -7.5
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-7.5, -5}