(2x+40)(2x+30)=3224

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Solution for (2x+40)(2x+30)=3224 equation: 


Simplifying
(2x + 40)(2x + 30) = 3224

Reorder the terms:
(40 + 2x)(2x + 30) = 3224

Reorder the terms:
(40 + 2x)(30 + 2x) = 3224

Multiply (40 + 2x) * (30 + 2x)
(40(30 + 2x) + 2x * (30 + 2x)) = 3224
((30 * 40 + 2x * 40) + 2x * (30 + 2x)) = 3224
((1200 + 80x) + 2x * (30 + 2x)) = 3224
(1200 + 80x + (30 * 2x + 2x * 2x)) = 3224
(1200 + 80x + (60x + 4x2)) = 3224

Combine like terms: 80x + 60x = 140x
(1200 + 140x + 4x2) = 3224

Solving
1200 + 140x + 4x2 = 3224

Solving for variable 'x'.

Reorder the terms:
1200 + -3224 + 140x + 4x2 = 3224 + -3224

Combine like terms: 1200 + -3224 = -2024
-2024 + 140x + 4x2 = 3224 + -3224

Combine like terms: 3224 + -3224 = 0
-2024 + 140x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-506 + 35x + x2) = 0

Factor a trinomial.
4((-46 + -1x)(11 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-46 + -1x)' equal to zero and attempt to solve:

Simplifying
-46 + -1x = 0

Solving
-46 + -1x = 0

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

Add '46' to each side of the equation.
-46 + 46 + -1x = 0 + 46

Combine like terms: -46 + 46 = 0
0 + -1x = 0 + 46
-1x = 0 + 46

Combine like terms: 0 + 46 = 46
-1x = 46

Divide each side by '-1'.
x = -46

Simplifying
x = -46

Subproblem 2
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11
Solution
x = {-46, 11}

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