x^2+13x+42=(x+g)(x+h)

Solution for x^2+13x+42=(x+g)(x+h) equation:

Simplifying
x2 + 13x + 42 = (x + g)(x + h)

Reorder the terms:
42 + 13x + x2 = (x + g)(x + h)

Reorder the terms:
42 + 13x + x2 = (g + x)(x + h)

Reorder the terms:
42 + 13x + x2 = (g + x)(h + x)

Multiply (g + x) * (h + x)
42 + 13x + x2 = (g(h + x) + x(h + x))
42 + 13x + x2 = ((h * g + x * g) + x(h + x))
42 + 13x + x2 = ((gh + gx) + x(h + x))
42 + 13x + x2 = (gh + gx + (h * x + x * x))
42 + 13x + x2 = (gh + gx + (hx + x2))
42 + 13x + x2 = (gh + gx + hx + x2)

Add '-1x2' to each side of the equation.
42 + 13x + x2 + -1x2 = gh + gx + hx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + 13x + 0 = gh + gx + hx + x2 + -1x2
42 + 13x = gh + gx + hx + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
42 + 13x = gh + gx + hx + 0
42 + 13x = gh + gx + hx

Solving
42 + 13x = gh + gx + hx

Solving for variable 'x'.

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

Add '-1gx' to each side of the equation.
42 + -1gx + 13x = gh + gx + -1gx + hx

Combine like terms: gx + -1gx = 0
42 + -1gx + 13x = gh + 0 + hx
42 + -1gx + 13x = gh + hx

Add '-1hx' to each side of the equation.
42 + -1gx + -1hx + 13x = gh + hx + -1hx

Combine like terms: hx + -1hx = 0
42 + -1gx + -1hx + 13x = gh + 0
42 + -1gx + -1hx + 13x = gh

Add '-42' to each side of the equation.
42 + -1gx + -1hx + -42 + 13x = -42 + gh

Reorder the terms:
42 + -42 + -1gx + -1hx + 13x = -42 + gh

Combine like terms: 42 + -42 = 0
0 + -1gx + -1hx + 13x = -42 + gh
-1gx + -1hx + 13x = -42 + gh

Reorder the terms:
42 + -1gh + -1gx + -1hx + 13x = -42 + gh + 42 + -1gh

Reorder the terms:
42 + -1gh + -1gx + -1hx + 13x = -42 + 42 + gh + -1gh

Combine like terms: -42 + 42 = 0
42 + -1gh + -1gx + -1hx + 13x = 0 + gh + -1gh
42 + -1gh + -1gx + -1hx + 13x = gh + -1gh

Combine like terms: gh + -1gh = 0
42 + -1gh + -1gx + -1hx + 13x = 0

The solution to this equation could not be determined.