(30+x)(15+x)=1000

Solution for (30+x)(15+x)=1000 equation:

Simplifying
(30 + x)(15 + x) = 1000

Multiply (30 + x) * (15 + x)
(30(15 + x) + x(15 + x)) = 1000
((15 * 30 + x * 30) + x(15 + x)) = 1000
((450 + 30x) + x(15 + x)) = 1000
(450 + 30x + (15 * x + x * x)) = 1000
(450 + 30x + (15x + x2)) = 1000

Combine like terms: 30x + 15x = 45x
(450 + 45x + x2) = 1000

Solving
450 + 45x + x2 = 1000

Solving for variable 'x'.

Reorder the terms:
450 + -1000 + 45x + x2 = 1000 + -1000

Combine like terms: 450 + -1000 = -550
-550 + 45x + x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-550 + 45x + x2 = 0

Factor a trinomial.
(-55 + -1x)(10 + -1x) = 0

Subproblem 1
Set the factor '(-55 + -1x)' equal to zero and attempt to solve:

Simplifying
-55 + -1x = 0

Solving
-55 + -1x = 0

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

Add '55' to each side of the equation.
-55 + 55 + -1x = 0 + 55

Combine like terms: -55 + 55 = 0
0 + -1x = 0 + 55
-1x = 0 + 55

Combine like terms: 0 + 55 = 55
-1x = 55

Divide each side by '-1'.
x = -55

Simplifying
x = -55
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 = {-55, 10}