42=(x+3)(x-8)

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Solution for 42=(x+3)(x-8) equation: 


Simplifying
42 = (x + 3)(x + -8)

Reorder the terms:
42 = (3 + x)(x + -8)

Reorder the terms:
42 = (3 + x)(-8 + x)

Multiply (3 + x) * (-8 + x)
42 = (3(-8 + x) + x(-8 + x))
42 = ((-8 * 3 + x * 3) + x(-8 + x))
42 = ((-24 + 3x) + x(-8 + x))
42 = (-24 + 3x + (-8 * x + x * x))
42 = (-24 + 3x + (-8x + x2))

Combine like terms: 3x + -8x = -5x
42 = (-24 + -5x + x2)

Solving
42 = -24 + -5x + x2

Solving for variable 'x'.

Combine like terms: 42 + 24 = 66
66 + 5x + -1x2 = -24 + -5x + x2 + 24 + 5x + -1x2

Reorder the terms:
66 + 5x + -1x2 = -24 + 24 + -5x + 5x + x2 + -1x2

Combine like terms: -24 + 24 = 0
66 + 5x + -1x2 = 0 + -5x + 5x + x2 + -1x2
66 + 5x + -1x2 = -5x + 5x + x2 + -1x2

Combine like terms: -5x + 5x = 0
66 + 5x + -1x2 = 0 + x2 + -1x2
66 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
66 + 5x + -1x2 = 0

Factor a trinomial.
(11 + -1x)(6 + x) = 0


Subproblem 1
Set the factor '(11 + -1x)' equal to zero and attempt to solve:

Simplifying
11 + -1x = 0

Solving
11 + -1x = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1x = 0 + -11
-1x = 0 + -11

Combine like terms: 0 + -11 = -11
-1x = -11

Divide each side by '-1'.
x = 11

Simplifying
x = 11

Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {11, -6}

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