3(10)(12)=(10+x)(12+x)

Solution for 3(10)(12)=(10+x)(12+x) equation:

Simplifying
3(10)(12) = (10 + x)(12 + x)

Multiply 3 * 10
30 * 12 = (10 + x)(12 + x)

Multiply 30 * 12
360 = (10 + x)(12 + x)

Multiply (10 + x) * (12 + x)
360 = (10(12 + x) + x(12 + x))
360 = ((12 * 10 + x * 10) + x(12 + x))
360 = ((120 + 10x) + x(12 + x))
360 = (120 + 10x + (12 * x + x * x))
360 = (120 + 10x + (12x + x2))

Combine like terms: 10x + 12x = 22x
360 = (120 + 22x + x2)

Solving
360 = 120 + 22x + x2

Solving for variable 'x'.

Combine like terms: 360 + -120 = 240
240 + -22x + -1x2 = 120 + 22x + x2 + -120 + -22x + -1x2

Reorder the terms:
240 + -22x + -1x2 = 120 + -120 + 22x + -22x + x2 + -1x2

Combine like terms: 120 + -120 = 0
240 + -22x + -1x2 = 0 + 22x + -22x + x2 + -1x2
240 + -22x + -1x2 = 22x + -22x + x2 + -1x2

Combine like terms: 22x + -22x = 0
240 + -22x + -1x2 = 0 + x2 + -1x2
240 + -22x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
240 + -22x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(30 + x) = 0

Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Subproblem 2
Set the factor '(30 + x)' equal to zero and attempt to solve:

Simplifying
30 + x = 0

Solving
30 + x = 0

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

Add '-30' to each side of the equation.
30 + -30 + x = 0 + -30

Combine like terms: 30 + -30 = 0
0 + x = 0 + -30
x = 0 + -30

Combine like terms: 0 + -30 = -30
x = -30

Simplifying
x = -30
Solution
x = {8, -30}