(x+3)(x+4)=30

Solution for (x+3)(x+4)=30 equation:

Simplifying
(x + 3)(x + 4) = 30

Reorder the terms:
(3 + x)(x + 4) = 30

Reorder the terms:
(3 + x)(4 + x) = 30

Multiply (3 + x) * (4 + x)
(3(4 + x) + x(4 + x)) = 30
((4 * 3 + x * 3) + x(4 + x)) = 30
((12 + 3x) + x(4 + x)) = 30
(12 + 3x + (4 * x + x * x)) = 30
(12 + 3x + (4x + x2)) = 30

Combine like terms: 3x + 4x = 7x
(12 + 7x + x2) = 30

Solving
12 + 7x + x2 = 30

Solving for variable 'x'.

Reorder the terms:
12 + -30 + 7x + x2 = 30 + -30

Combine like terms: 12 + -30 = -18
-18 + 7x + x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-18 + 7x + x2 = 0

Factor a trinomial.
(-9 + -1x)(2 + -1x) = 0

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
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
Solution
x = {-9, 2}