(3+X)(14-3X)=30

Solution for (3+X)(14-3X)=30 equation:

Simplifying
(3 + X)(14 + -3X) = 30

Multiply (3 + X) * (14 + -3X)
(3(14 + -3X) + X(14 + -3X)) = 30
((14 * 3 + -3X * 3) + X(14 + -3X)) = 30
((42 + -9X) + X(14 + -3X)) = 30
(42 + -9X + (14 * X + -3X * X)) = 30
(42 + -9X + (14X + -3X2)) = 30

Combine like terms: -9X + 14X = 5X
(42 + 5X + -3X2) = 30

Solving
42 + 5X + -3X2 = 30

Solving for variable 'X'.

Reorder the terms:
42 + -30 + 5X + -3X2 = 30 + -30

Combine like terms: 42 + -30 = 12
12 + 5X + -3X2 = 30 + -30

Combine like terms: 30 + -30 = 0
12 + 5X + -3X2 = 0

Factor a trinomial.
(3 + -1X)(4 + 3X) = 0

Subproblem 1
Set the factor '(3 + -1X)' equal to zero and attempt to solve:

Simplifying
3 + -1X = 0

Solving
3 + -1X = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1X = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1X = 0 + -3
-1X = 0 + -3

Combine like terms: 0 + -3 = -3
-1X = -3

Divide each side by '-1'.
X = 3

Simplifying
X = 3
Subproblem 2
Set the factor '(4 + 3X)' equal to zero and attempt to solve:

Simplifying
4 + 3X = 0

Solving
4 + 3X = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3X = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3X = 0 + -4
3X = 0 + -4

Combine like terms: 0 + -4 = -4
3X = -4

Divide each side by '3'.
X = -1.333333333

Simplifying
X = -1.333333333
Solution
X = {3, -1.333333333}