416=(2x+40)(2x+60)-2400

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Solution for 416=(2x+40)(2x+60)-2400 equation: 


Simplifying
416 = (2x + 40)(2x + 60) + -2400

Reorder the terms:
416 = (40 + 2x)(2x + 60) + -2400

Reorder the terms:
416 = (40 + 2x)(60 + 2x) + -2400

Multiply (40 + 2x) * (60 + 2x)
416 = (40(60 + 2x) + 2x * (60 + 2x)) + -2400
416 = ((60 * 40 + 2x * 40) + 2x * (60 + 2x)) + -2400
416 = ((2400 + 80x) + 2x * (60 + 2x)) + -2400
416 = (2400 + 80x + (60 * 2x + 2x * 2x)) + -2400
416 = (2400 + 80x + (120x + 4x2)) + -2400

Combine like terms: 80x + 120x = 200x
416 = (2400 + 200x + 4x2) + -2400

Reorder the terms:
416 = 2400 + -2400 + 200x + 4x2

Combine like terms: 2400 + -2400 = 0
416 = 0 + 200x + 4x2
416 = 200x + 4x2

Solving
416 = 200x + 4x2

Solving for variable 'x'.

Reorder the terms:
416 + -200x + -4x2 = 200x + -200x + 4x2 + -4x2

Combine like terms: 200x + -200x = 0
416 + -200x + -4x2 = 0 + 4x2 + -4x2
416 + -200x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
416 + -200x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(104 + -50x + -1x2) = 0

Factor a trinomial.
4((2 + -1x)(52 + x)) = 0

Ignore the factor 4.

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 2
Set the factor '(52 + x)' equal to zero and attempt to solve:

Simplifying
52 + x = 0

Solving
52 + x = 0

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

Add '-52' to each side of the equation.
52 + -52 + x = 0 + -52

Combine like terms: 52 + -52 = 0
0 + x = 0 + -52
x = 0 + -52

Combine like terms: 0 + -52 = -52
x = -52

Simplifying
x = -52
Solution
x = {2, -52}

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