(20+2x)(30+2x)=1064

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Solution for (20+2x)(30+2x)=1064 equation: 


Simplifying
(20 + 2x)(30 + 2x) = 1064

Multiply (20 + 2x) * (30 + 2x)
(20(30 + 2x) + 2x * (30 + 2x)) = 1064
((30 * 20 + 2x * 20) + 2x * (30 + 2x)) = 1064
((600 + 40x) + 2x * (30 + 2x)) = 1064
(600 + 40x + (30 * 2x + 2x * 2x)) = 1064
(600 + 40x + (60x + 4x2)) = 1064

Combine like terms: 40x + 60x = 100x
(600 + 100x + 4x2) = 1064

Solving
600 + 100x + 4x2 = 1064

Solving for variable 'x'.

Reorder the terms:
600 + -1064 + 100x + 4x2 = 1064 + -1064

Combine like terms: 600 + -1064 = -464
-464 + 100x + 4x2 = 1064 + -1064

Combine like terms: 1064 + -1064 = 0
-464 + 100x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-116 + 25x + x2) = 0

Factor a trinomial.
4((-29 + -1x)(4 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-29 + -1x)' equal to zero and attempt to solve:

Simplifying
-29 + -1x = 0

Solving
-29 + -1x = 0

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

Add '29' to each side of the equation.
-29 + 29 + -1x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + -1x = 0 + 29
-1x = 0 + 29

Combine like terms: 0 + 29 = 29
-1x = 29

Divide each side by '-1'.
x = -29

Simplifying
x = -29

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-29, 4}

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