(5+x)(x)=150

Solution for (5+x)(x)=150 equation:

Simplifying
(5 + x)(x) = 150

Reorder the terms for easier multiplication:
x(5 + x) = 150
(5 * x + x * x) = 150
(5x + x2) = 150

Solving
5x + x2 = 150

Solving for variable 'x'.

Reorder the terms:
-150 + 5x + x2 = 150 + -150

Combine like terms: 150 + -150 = 0
-150 + 5x + x2 = 0

Factor a trinomial.
(-15 + -1x)(10 + -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 '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

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

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

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-15, 10}