(10+2x)(30+2x)=800

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Solution for (10+2x)(30+2x)=800 equation: 


Simplifying
(10 + 2x)(30 + 2x) = 800

Multiply (10 + 2x) * (30 + 2x)
(10(30 + 2x) + 2x * (30 + 2x)) = 800
((30 * 10 + 2x * 10) + 2x * (30 + 2x)) = 800
((300 + 20x) + 2x * (30 + 2x)) = 800
(300 + 20x + (30 * 2x + 2x * 2x)) = 800
(300 + 20x + (60x + 4x2)) = 800

Combine like terms: 20x + 60x = 80x
(300 + 80x + 4x2) = 800

Solving
300 + 80x + 4x2 = 800

Solving for variable 'x'.

Reorder the terms:
300 + -800 + 80x + 4x2 = 800 + -800

Combine like terms: 300 + -800 = -500
-500 + 80x + 4x2 = 800 + -800

Combine like terms: 800 + -800 = 0
-500 + 80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-125 + 20x + x2) = 0

Factor a trinomial.
4((-25 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-25 + -1x)' equal to zero and attempt to solve:

Simplifying
-25 + -1x = 0

Solving
-25 + -1x = 0

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

Add '25' to each side of the equation.
-25 + 25 + -1x = 0 + 25

Combine like terms: -25 + 25 = 0
0 + -1x = 0 + 25
-1x = 0 + 25

Combine like terms: 0 + 25 = 25
-1x = 25

Divide each side by '-1'.
x = -25

Simplifying
x = -25

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-25, 5}

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