(40+x)(50+x)=3000

Solution for (40+x)(50+x)=3000 equation:

Simplifying
(40 + x)(50 + x) = 3000

Multiply (40 + x) * (50 + x)
(40(50 + x) + x(50 + x)) = 3000
((50 * 40 + x * 40) + x(50 + x)) = 3000
((2000 + 40x) + x(50 + x)) = 3000
(2000 + 40x + (50 * x + x * x)) = 3000
(2000 + 40x + (50x + x2)) = 3000

Combine like terms: 40x + 50x = 90x
(2000 + 90x + x2) = 3000

Solving
2000 + 90x + x2 = 3000

Solving for variable 'x'.

Reorder the terms:
2000 + -3000 + 90x + x2 = 3000 + -3000

Combine like terms: 2000 + -3000 = -1000
-1000 + 90x + x2 = 3000 + -3000

Combine like terms: 3000 + -3000 = 0
-1000 + 90x + x2 = 0

Factor a trinomial.
(-100 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-100 + -1x)' equal to zero and attempt to solve:

Simplifying
-100 + -1x = 0

Solving
-100 + -1x = 0

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

Add '100' to each side of the equation.
-100 + 100 + -1x = 0 + 100

Combine like terms: -100 + 100 = 0
0 + -1x = 0 + 100
-1x = 0 + 100

Combine like terms: 0 + 100 = 100
-1x = 100

Divide each side by '-1'.
x = -100

Simplifying
x = -100
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 = {-100, 10}