42-(x+3)(x+4)=0

Solution for 42-(x+3)(x+4)=0 equation:

Simplifying
42 + -1(x + 3)(x + 4) = 0

Reorder the terms:
42 + -1(3 + x)(x + 4) = 0

Reorder the terms:
42 + -1(3 + x)(4 + x) = 0

Multiply (3 + x) * (4 + x)
42 + -1(3(4 + x) + x(4 + x)) = 0
42 + -1((4 * 3 + x * 3) + x(4 + x)) = 0
42 + -1((12 + 3x) + x(4 + x)) = 0
42 + -1(12 + 3x + (4 * x + x * x)) = 0
42 + -1(12 + 3x + (4x + x2)) = 0

Combine like terms: 3x + 4x = 7x
42 + -1(12 + 7x + x2) = 0
42 + (12 * -1 + 7x * -1 + x2 * -1) = 0
42 + (-12 + -7x + -1x2) = 0

Combine like terms: 42 + -12 = 30
30 + -7x + -1x2 = 0

Solving
30 + -7x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -1x)(10 + x) = 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 '(10 + x)' equal to zero and attempt to solve:

Simplifying
10 + x = 0

Solving
10 + x = 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 + x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + x = 0 + -10
x = 0 + -10

Combine like terms: 0 + -10 = -10
x = -10

Simplifying
x = -10
Solution
x = {3, -10}