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

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


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

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

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

Solving
1000 = 450 + 45x + x2

Solving for variable 'x'.

Combine like terms: 1000 + -450 = 550
550 + -45x + -1x2 = 450 + 45x + x2 + -450 + -45x + -1x2

Reorder the terms:
550 + -45x + -1x2 = 450 + -450 + 45x + -45x + x2 + -1x2

Combine like terms: 450 + -450 = 0
550 + -45x + -1x2 = 0 + 45x + -45x + x2 + -1x2
550 + -45x + -1x2 = 45x + -45x + x2 + -1x2

Combine like terms: 45x + -45x = 0
550 + -45x + -1x2 = 0 + x2 + -1x2
550 + -45x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
550 + -45x + -1x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(55 + x)' equal to zero and attempt to solve:

Simplifying
55 + x = 0

Solving
55 + x = 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 + x = 0 + -55

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

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

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

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