(25+x)(10+x)=1000

Solution for (25+x)(10+x)=1000 equation:

Simplifying
(25 + x)(10 + x) = 1000

Multiply (25 + x) * (10 + x)
(25(10 + x) + x(10 + x)) = 1000
((10 * 25 + x * 25) + x(10 + x)) = 1000
((250 + 25x) + x(10 + x)) = 1000
(250 + 25x + (10 * x + x * x)) = 1000
(250 + 25x + (10x + x2)) = 1000

Combine like terms: 25x + 10x = 35x
(250 + 35x + x2) = 1000

Solving
250 + 35x + x2 = 1000

Solving for variable 'x'.

Reorder the terms:
250 + -1000 + 35x + x2 = 1000 + -1000

Combine like terms: 250 + -1000 = -750
-750 + 35x + x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-750 + 35x + x2 = 0

Factor a trinomial.
(-50 + -1x)(15 + -1x) = 0

Subproblem 1
Set the factor '(-50 + -1x)' equal to zero and attempt to solve:

Simplifying
-50 + -1x = 0

Solving
-50 + -1x = 0

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

Add '50' to each side of the equation.
-50 + 50 + -1x = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -1x = 0 + 50
-1x = 0 + 50

Combine like terms: 0 + 50 = 50
-1x = 50

Divide each side by '-1'.
x = -50

Simplifying
x = -50
Subproblem 2
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
Solution
x = {-50, 15}