(24+2x)(8+2x)-420=0

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Solution for (24+2x)(8+2x)-420=0 equation: 


Simplifying
(24 + 2x)(8 + 2x) + -420 = 0

Multiply (24 + 2x) * (8 + 2x)
(24(8 + 2x) + 2x * (8 + 2x)) + -420 = 0
((8 * 24 + 2x * 24) + 2x * (8 + 2x)) + -420 = 0
((192 + 48x) + 2x * (8 + 2x)) + -420 = 0
(192 + 48x + (8 * 2x + 2x * 2x)) + -420 = 0
(192 + 48x + (16x + 4x2)) + -420 = 0

Combine like terms: 48x + 16x = 64x
(192 + 64x + 4x2) + -420 = 0

Reorder the terms:
192 + -420 + 64x + 4x2 = 0

Combine like terms: 192 + -420 = -228
-228 + 64x + 4x2 = 0

Solving
-228 + 64x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-57 + 16x + x2) = 0

Factor a trinomial.
4((-19 + -1x)(3 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-19 + -1x)' equal to zero and attempt to solve:

Simplifying
-19 + -1x = 0

Solving
-19 + -1x = 0

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

Add '19' to each side of the equation.
-19 + 19 + -1x = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -1x = 0 + 19
-1x = 0 + 19

Combine like terms: 0 + 19 = 19
-1x = 19

Divide each side by '-1'.
x = -19

Simplifying
x = -19

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-19, 3}

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