(x+9)(x+10)=42

Solution for (x+9)(x+10)=42 equation:

Simplifying
(x + 9)(x + 10) = 42

Reorder the terms:
(9 + x)(x + 10) = 42

Reorder the terms:
(9 + x)(10 + x) = 42

Multiply (9 + x) * (10 + x)
(9(10 + x) + x(10 + x)) = 42
((10 * 9 + x * 9) + x(10 + x)) = 42
((90 + 9x) + x(10 + x)) = 42
(90 + 9x + (10 * x + x * x)) = 42
(90 + 9x + (10x + x2)) = 42

Combine like terms: 9x + 10x = 19x
(90 + 19x + x2) = 42

Solving
90 + 19x + x2 = 42

Solving for variable 'x'.

Reorder the terms:
90 + -42 + 19x + x2 = 42 + -42

Combine like terms: 90 + -42 = 48
48 + 19x + x2 = 42 + -42

Combine like terms: 42 + -42 = 0
48 + 19x + x2 = 0

Factor a trinomial.
(16 + x)(3 + x) = 0

Subproblem 1
Set the factor '(16 + x)' equal to zero and attempt to solve:

Simplifying
16 + x = 0

Solving
16 + x = 0

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

Add '-16' to each side of the equation.
16 + -16 + x = 0 + -16

Combine like terms: 16 + -16 = 0
0 + x = 0 + -16
x = 0 + -16

Combine like terms: 0 + -16 = -16
x = -16

Simplifying
x = -16
Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-16, -3}