(10+2x)(5+2x)=84

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Solution for (10+2x)(5+2x)=84 equation: 


Simplifying
(10 + 2x)(5 + 2x) = 84

Multiply (10 + 2x) * (5 + 2x)
(10(5 + 2x) + 2x * (5 + 2x)) = 84
((5 * 10 + 2x * 10) + 2x * (5 + 2x)) = 84
((50 + 20x) + 2x * (5 + 2x)) = 84
(50 + 20x + (5 * 2x + 2x * 2x)) = 84
(50 + 20x + (10x + 4x2)) = 84

Combine like terms: 20x + 10x = 30x
(50 + 30x + 4x2) = 84

Solving
50 + 30x + 4x2 = 84

Solving for variable 'x'.

Reorder the terms:
50 + -84 + 30x + 4x2 = 84 + -84

Combine like terms: 50 + -84 = -34
-34 + 30x + 4x2 = 84 + -84

Combine like terms: 84 + -84 = 0
-34 + 30x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + 15x + 2x2) = 0

Factor a trinomial.
2((-17 + -2x)(1 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + -2x)' equal to zero and attempt to solve:

Simplifying
-17 + -2x = 0

Solving
-17 + -2x = 0

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

Add '17' to each side of the equation.
-17 + 17 + -2x = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -2x = 0 + 17
-2x = 0 + 17

Combine like terms: 0 + 17 = 17
-2x = 17

Divide each side by '-2'.
x = -8.5

Simplifying
x = -8.5

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 = {-8.5, 1}

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