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

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

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

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

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

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

Combine like terms: -3x + -4x = -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.
(-3 + -1x)(10 + -1x) = 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 + -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
Solution
x = {-3, 10}