(33+x)(45+x)=

Solution for (33+x)(45+x)= equation:

Simplifying
(33 + x)(45 + x) = 0

Multiply (33 + x) * (45 + x)
(33(45 + x) + x(45 + x)) = 0
((45 * 33 + x * 33) + x(45 + x)) = 0
((1485 + 33x) + x(45 + x)) = 0
(1485 + 33x + (45 * x + x * x)) = 0
(1485 + 33x + (45x + x2)) = 0

Combine like terms: 33x + 45x = 78x
(1485 + 78x + x2) = 0

Solving
1485 + 78x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(45 + x)(33 + x) = 0

Subproblem 1
Set the factor '(45 + x)' equal to zero and attempt to solve:

Simplifying
45 + x = 0

Solving
45 + x = 0

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

Add '-45' to each side of the equation.
45 + -45 + x = 0 + -45

Combine like terms: 45 + -45 = 0
0 + x = 0 + -45
x = 0 + -45

Combine like terms: 0 + -45 = -45
x = -45

Simplifying
x = -45
Subproblem 2
Set the factor '(33 + x)' equal to zero and attempt to solve:

Simplifying
33 + x = 0

Solving
33 + x = 0

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

Add '-33' to each side of the equation.
33 + -33 + x = 0 + -33

Combine like terms: 33 + -33 = 0
0 + x = 0 + -33
x = 0 + -33

Combine like terms: 0 + -33 = -33
x = -33

Simplifying
x = -33
Solution
x = {-45, -33}