X^2+7x+12=(x+g)(x+h)

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Solution for X^2+7x+12=(x+g)(x+h) equation: 


Simplifying
X2 + 7x + 12 = (x + g)(x + h)

Reorder the terms:
12 + X2 + 7x = (x + g)(x + h)

Reorder the terms:
12 + X2 + 7x = (g + x)(x + h)

Reorder the terms:
12 + X2 + 7x = (g + x)(h + x)

Multiply (g + x) * (h + x)
12 + X2 + 7x = (g(h + x) + x(h + x))
12 + X2 + 7x = ((h * g + x * g) + x(h + x))
12 + X2 + 7x = ((gh + gx) + x(h + x))
12 + X2 + 7x = (gh + gx + (h * x + x * x))
12 + X2 + 7x = (gh + gx + (hx + x2))
12 + X2 + 7x = (gh + gx + hx + x2)

Solving
12 + X2 + 7x = gh + gx + hx + x2

Solving for variable 'X'.

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

Add '-12' to each side of the equation.
12 + X2 + -12 + 7x = gh + gx + hx + -12 + x2

Reorder the terms:
12 + -12 + X2 + 7x = gh + gx + hx + -12 + x2

Combine like terms: 12 + -12 = 0
0 + X2 + 7x = gh + gx + hx + -12 + x2
X2 + 7x = gh + gx + hx + -12 + x2

Reorder the terms:
X2 + 7x = -12 + gh + gx + hx + x2

Add '-7x' to each side of the equation.
X2 + 7x + -7x = -12 + gh + gx + hx + -7x + x2

Combine like terms: 7x + -7x = 0
X2 + 0 = -12 + gh + gx + hx + -7x + x2
X2 = -12 + gh + gx + hx + -7x + x2

Simplifying
X2 = -12 + gh + gx + hx + -7x + x2

Reorder the terms:
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = -12 + gh + gx + hx + -7x + x2 + 12 + -1gh + -1gx + -1hx + 7x + -1x2

Reorder the terms:
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = -12 + 12 + gh + -1gh + gx + -1gx + hx + -1hx + -7x + 7x + x2 + -1x2

Combine like terms: -12 + 12 = 0
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = 0 + gh + -1gh + gx + -1gx + hx + -1hx + -7x + 7x + x2 + -1x2
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = gh + -1gh + gx + -1gx + hx + -1hx + -7x + 7x + x2 + -1x2

Combine like terms: gh + -1gh = 0
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = 0 + gx + -1gx + hx + -1hx + -7x + 7x + x2 + -1x2
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = gx + -1gx + hx + -1hx + -7x + 7x + x2 + -1x2

Combine like terms: gx + -1gx = 0
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = 0 + hx + -1hx + -7x + 7x + x2 + -1x2
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = hx + -1hx + -7x + 7x + x2 + -1x2

Combine like terms: hx + -1hx = 0
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = 0 + -7x + 7x + x2 + -1x2
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = -7x + 7x + x2 + -1x2

Combine like terms: -7x + 7x = 0
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = 0 + x2 + -1x2
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + X2 + -1gh + -1gx + -1hx + 7x + -1x2 = 0

The solution to this equation could not be determined.

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