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

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

Simplifying
2(40)(60) = (x + 40)(x + 60)

Multiply 2 * 40
80 * 60 = (x + 40)(x + 60)

Multiply 80 * 60
4800 = (x + 40)(x + 60)

Reorder the terms:
4800 = (40 + x)(x + 60)

Reorder the terms:
4800 = (40 + x)(60 + x)

Multiply (40 + x) * (60 + x)
4800 = (40(60 + x) + x(60 + x))
4800 = ((60 * 40 + x * 40) + x(60 + x))
4800 = ((2400 + 40x) + x(60 + x))
4800 = (2400 + 40x + (60 * x + x * x))
4800 = (2400 + 40x + (60x + x2))

Combine like terms: 40x + 60x = 100x
4800 = (2400 + 100x + x2)

Solving
4800 = 2400 + 100x + x2

Solving for variable 'x'.

Combine like terms: 4800 + -2400 = 2400
2400 + -100x + -1x2 = 2400 + 100x + x2 + -2400 + -100x + -1x2

Reorder the terms:
2400 + -100x + -1x2 = 2400 + -2400 + 100x + -100x + x2 + -1x2

Combine like terms: 2400 + -2400 = 0
2400 + -100x + -1x2 = 0 + 100x + -100x + x2 + -1x2
2400 + -100x + -1x2 = 100x + -100x + x2 + -1x2

Combine like terms: 100x + -100x = 0
2400 + -100x + -1x2 = 0 + x2 + -1x2
2400 + -100x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2400 + -100x + -1x2 = 0

Factor a trinomial.
(20 + -1x)(120 + x) = 0

Subproblem 1
Set the factor '(20 + -1x)' equal to zero and attempt to solve:

Simplifying
20 + -1x = 0

Solving
20 + -1x = 0

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

Add '-20' to each side of the equation.
20 + -20 + -1x = 0 + -20

Combine like terms: 20 + -20 = 0
0 + -1x = 0 + -20
-1x = 0 + -20

Combine like terms: 0 + -20 = -20
-1x = -20

Divide each side by '-1'.
x = 20

Simplifying
x = 20
Subproblem 2
Set the factor '(120 + x)' equal to zero and attempt to solve:

Simplifying
120 + x = 0

Solving
120 + x = 0

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

Add '-120' to each side of the equation.
120 + -120 + x = 0 + -120

Combine like terms: 120 + -120 = 0
0 + x = 0 + -120
x = 0 + -120

Combine like terms: 0 + -120 = -120
x = -120

Simplifying
x = -120
Solution
x = {20, -120}