(20+x)(30+x)=1064

Solution for (20+x)(30+x)=1064 equation:

Simplifying
(20 + x)(30 + x) = 1064

Multiply (20 + x) * (30 + x)
(20(30 + x) + x(30 + x)) = 1064
((30 * 20 + x * 20) + x(30 + x)) = 1064
((600 + 20x) + x(30 + x)) = 1064
(600 + 20x + (30 * x + x * x)) = 1064
(600 + 20x + (30x + x2)) = 1064

Combine like terms: 20x + 30x = 50x
(600 + 50x + x2) = 1064

Solving
600 + 50x + x2 = 1064

Solving for variable 'x'.

Reorder the terms:
600 + -1064 + 50x + x2 = 1064 + -1064

Combine like terms: 600 + -1064 = -464
-464 + 50x + x2 = 1064 + -1064

Combine like terms: 1064 + -1064 = 0
-464 + 50x + x2 = 0

Factor a trinomial.
(-58 + -1x)(8 + -1x) = 0

Subproblem 1
Set the factor '(-58 + -1x)' equal to zero and attempt to solve:

Simplifying
-58 + -1x = 0

Solving
-58 + -1x = 0

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

Add '58' to each side of the equation.
-58 + 58 + -1x = 0 + 58

Combine like terms: -58 + 58 = 0
0 + -1x = 0 + 58
-1x = 0 + 58

Combine like terms: 0 + 58 = 58
-1x = 58

Divide each side by '-1'.
x = -58

Simplifying
x = -58
Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-58, 8}