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

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

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

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

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

Solving
1000 = 250 + 35x + x2

Solving for variable 'x'.

Combine like terms: 1000 + -250 = 750
750 + -35x + -1x2 = 250 + 35x + x2 + -250 + -35x + -1x2

Reorder the terms:
750 + -35x + -1x2 = 250 + -250 + 35x + -35x + x2 + -1x2

Combine like terms: 250 + -250 = 0
750 + -35x + -1x2 = 0 + 35x + -35x + x2 + -1x2
750 + -35x + -1x2 = 35x + -35x + x2 + -1x2

Combine like terms: 35x + -35x = 0
750 + -35x + -1x2 = 0 + x2 + -1x2
750 + -35x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
750 + -35x + -1x2 = 0

Factor a trinomial.
(15 + -1x)(50 + x) = 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 '(50 + x)' equal to zero and attempt to solve:

Simplifying
50 + x = 0

Solving
50 + x = 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 + x = 0 + -50

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

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

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