[(2x+25)(2x+13)]-(25*13)=480

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Solution for [(2x+25)(2x+13)]-(25*13)=480 equation: 


Simplifying
[(2x + 25)(2x + 13)] + -1(25 * 13) = 480

Reorder the terms:
[(25 + 2x)(2x + 13)] + -1(25 * 13) = 480

Reorder the terms:
[(25 + 2x)(13 + 2x)] + -1(25 * 13) = 480

Multiply (25 + 2x) * (13 + 2x)
[(25(13 + 2x) + 2x * (13 + 2x))] + -1(25 * 13) = 480
[((13 * 25 + 2x * 25) + 2x * (13 + 2x))] + -1(25 * 13) = 480
[((325 + 50x) + 2x * (13 + 2x))] + -1(25 * 13) = 480
[(325 + 50x + (13 * 2x + 2x * 2x))] + -1(25 * 13) = 480
[(325 + 50x + (26x + 4x2))] + -1(25 * 13) = 480

Combine like terms: 50x + 26x = 76x
[(325 + 76x + 4x2)] + -1(25 * 13) = 480
[325 + 76x + 4x2] + -1(25 * 13) = 480

Remove brackets around [325 + 76x + 4x2]
325 + 76x + 4x2 + -1(25 * 13) = 480

Multiply 25 * 13
325 + 76x + 4x2 + -1(325) = 480

Multiply -1 * 325
325 + 76x + 4x2 + -325 = 480

Reorder the terms:
325 + -325 + 76x + 4x2 = 480

Combine like terms: 325 + -325 = 0
0 + 76x + 4x2 = 480
76x + 4x2 = 480

Solving
76x + 4x2 = 480

Solving for variable 'x'.

Reorder the terms:
-480 + 76x + 4x2 = 480 + -480

Combine like terms: 480 + -480 = 0
-480 + 76x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-120 + 19x + x2) = 0

Factor a trinomial.
4((-24 + -1x)(5 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve:

Simplifying
-24 + -1x = 0

Solving
-24 + -1x = 0

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

Add '24' to each side of the equation.
-24 + 24 + -1x = 0 + 24

Combine like terms: -24 + 24 = 0
0 + -1x = 0 + 24
-1x = 0 + 24

Combine like terms: 0 + 24 = 24
-1x = 24

Divide each side by '-1'.
x = -24

Simplifying
x = -24

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-24, 5}

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