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

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


Simplifying
(40 + 2x)(60 + 2x) + -1(60)(40) = 2400

Multiply (40 + 2x) * (60 + 2x)
(40(60 + 2x) + 2x * (60 + 2x)) + -1(60)(40) = 2400
((60 * 40 + 2x * 40) + 2x * (60 + 2x)) + -1(60)(40) = 2400
((2400 + 80x) + 2x * (60 + 2x)) + -1(60)(40) = 2400
(2400 + 80x + (60 * 2x + 2x * 2x)) + -1(60)(40) = 2400
(2400 + 80x + (120x + 4x2)) + -1(60)(40) = 2400

Combine like terms: 80x + 120x = 200x
(2400 + 200x + 4x2) + -1(60)(40) = 2400

Multiply -1 * 60
2400 + 200x + 4x2 + -60 * 40 = 2400

Multiply -60 * 40
2400 + 200x + 4x2 + -2400 = 2400

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

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

Solving
200x + 4x2 = 2400

Solving for variable 'x'.

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

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

Factor out the Greatest Common Factor (GCF), '4'.
4(-600 + 50x + x2) = 0

Factor a trinomial.
4((-60 + -1x)(10 + -1x)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(-60 + -1x)' equal to zero and attempt to solve:

Simplifying
-60 + -1x = 0

Solving
-60 + -1x = 0

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

Add '60' to each side of the equation.
-60 + 60 + -1x = 0 + 60

Combine like terms: -60 + 60 = 0
0 + -1x = 0 + 60
-1x = 0 + 60

Combine like terms: 0 + 60 = 60
-1x = 60

Divide each side by '-1'.
x = -60

Simplifying
x = -60

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-60, 10}

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