(8+2x)(10+2x)=120

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Solution for (8+2x)(10+2x)=120 equation: 


Simplifying
(8 + 2x)(10 + 2x) = 120

Multiply (8 + 2x) * (10 + 2x)
(8(10 + 2x) + 2x * (10 + 2x)) = 120
((10 * 8 + 2x * 8) + 2x * (10 + 2x)) = 120
((80 + 16x) + 2x * (10 + 2x)) = 120
(80 + 16x + (10 * 2x + 2x * 2x)) = 120
(80 + 16x + (20x + 4x2)) = 120

Combine like terms: 16x + 20x = 36x
(80 + 36x + 4x2) = 120

Solving
80 + 36x + 4x2 = 120

Solving for variable 'x'.

Reorder the terms:
80 + -120 + 36x + 4x2 = 120 + -120

Combine like terms: 80 + -120 = -40
-40 + 36x + 4x2 = 120 + -120

Combine like terms: 120 + -120 = 0
-40 + 36x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + 9x + x2) = 0

Factor a trinomial.
4((-10 + -1x)(1 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {-10, 1}

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