(x+4)(x+3)=42

Solution for (x+4)(x+3)=42 equation:

Simplifying
(x + 4)(x + 3) = 42

Reorder the terms:
(4 + x)(x + 3) = 42

Reorder the terms:
(4 + x)(3 + x) = 42

Multiply (4 + x) * (3 + x)
(4(3 + x) + x(3 + x)) = 42
((3 * 4 + x * 4) + x(3 + x)) = 42
((12 + 4x) + x(3 + x)) = 42
(12 + 4x + (3 * x + x * x)) = 42
(12 + 4x + (3x + x2)) = 42

Combine like terms: 4x + 3x = 7x
(12 + 7x + x2) = 42

Solving
12 + 7x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
12 + -42 + 7x + x2 = 42 + -42

Combine like terms: 12 + -42 = -30
-30 + 7x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
-30 + 7x + x2 = 0

Factor a trinomial.
(-10 + -1x)(3 + -1x) = 0

Subproblem 1
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
Subproblem 2
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
Solution
x = {-10, 3}