(10+2x)(30+2x)=1196

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Solution for (10+2x)(30+2x)=1196 equation: 


Simplifying
(10 + 2x)(30 + 2x) = 1196

Multiply (10 + 2x) * (30 + 2x)
(10(30 + 2x) + 2x * (30 + 2x)) = 1196
((30 * 10 + 2x * 10) + 2x * (30 + 2x)) = 1196
((300 + 20x) + 2x * (30 + 2x)) = 1196
(300 + 20x + (30 * 2x + 2x * 2x)) = 1196
(300 + 20x + (60x + 4x2)) = 1196

Combine like terms: 20x + 60x = 80x
(300 + 80x + 4x2) = 1196

Solving
300 + 80x + 4x2 = 1196

Solving for variable 'x'.

Reorder the terms:
300 + -1196 + 80x + 4x2 = 1196 + -1196

Combine like terms: 300 + -1196 = -896
-896 + 80x + 4x2 = 1196 + -1196

Combine like terms: 1196 + -1196 = 0
-896 + 80x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-224 + 20x + x2) = 0

Factor a trinomial.
4((-28 + -1x)(8 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-28 + -1x)' equal to zero and attempt to solve:

Simplifying
-28 + -1x = 0

Solving
-28 + -1x = 0

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

Add '28' to each side of the equation.
-28 + 28 + -1x = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -1x = 0 + 28
-1x = 0 + 28

Combine like terms: 0 + 28 = 28
-1x = 28

Divide each side by '-1'.
x = -28

Simplifying
x = -28

Subproblem 2
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
Solution
x = {-28, 8}

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