2x(x+5)=75+x^2

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

Simplifying
2x(x + 5) = 75 + x2

Reorder the terms:
2x(5 + x) = 75 + x2
(5 * 2x + x * 2x) = 75 + x2
(10x + 2x2) = 75 + x2

Solving
10x + 2x2 = 75 + x2

Solving for variable 'x'.

Reorder the terms:
-75 + 10x + 2x2 + -1x2 = 75 + x2 + -75 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-75 + 10x + 1x2 = 75 + x2 + -75 + -1x2

Reorder the terms:
-75 + 10x + 1x2 = 75 + -75 + x2 + -1x2

Combine like terms: 75 + -75 = 0
-75 + 10x + 1x2 = 0 + x2 + -1x2
-75 + 10x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-75 + 10x + 1x2 = 0

Factor a trinomial.
(-15 + -1x)(5 + -1x) = 0

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

Simplifying
-15 + -1x = 0

Solving
-15 + -1x = 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 + -1x = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1x = 0 + 15
-1x = 0 + 15

Combine like terms: 0 + 15 = 15
-1x = 15

Divide each side by '-1'.
x = -15

Simplifying
x = -15
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 = {-15, 5}