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

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


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

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

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

Solving
1064 = 600 + 50x + x2

Solving for variable 'x'.

Combine like terms: 1064 + -600 = 464
464 + -50x + -1x2 = 600 + 50x + x2 + -600 + -50x + -1x2

Reorder the terms:
464 + -50x + -1x2 = 600 + -600 + 50x + -50x + x2 + -1x2

Combine like terms: 600 + -600 = 0
464 + -50x + -1x2 = 0 + 50x + -50x + x2 + -1x2
464 + -50x + -1x2 = 50x + -50x + x2 + -1x2

Combine like terms: 50x + -50x = 0
464 + -50x + -1x2 = 0 + x2 + -1x2
464 + -50x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
464 + -50x + -1x2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(58 + x)' equal to zero and attempt to solve:

Simplifying
58 + x = 0

Solving
58 + x = 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 + x = 0 + -58

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

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

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

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