2x^2+5x=75

Solution for 2x^2+5x=75 equation:

Simplifying
2x2 + 5x = 75

Reorder the terms:
5x + 2x2 = 75

Solving
5x + 2x2 = 75

Solving for variable 'x'.

Reorder the terms:
-75 + 5x + 2x2 = 75 + -75

Combine like terms: 75 + -75 = 0
-75 + 5x + 2x2 = 0

Factor a trinomial.
(-15 + -2x)(5 + -1x) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

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