(t+2)(t+3)=(t+4)x(t+4)

Solution for (t+2)(t+3)=(t+4)x(t+4) equation:

Simplifying
(t + 2)(t + 3) = (t + 4) * x(t + 4)

Reorder the terms:
(2 + t)(t + 3) = (t + 4) * x(t + 4)

Reorder the terms:
(2 + t)(3 + t) = (t + 4) * x(t + 4)

Multiply (2 + t) * (3 + t)
(2(3 + t) + t(3 + t)) = (t + 4) * x(t + 4)
((3 * 2 + t * 2) + t(3 + t)) = (t + 4) * x(t + 4)
((6 + 2t) + t(3 + t)) = (t + 4) * x(t + 4)
(6 + 2t + (3 * t + t * t)) = (t + 4) * x(t + 4)
(6 + 2t + (3t + t2)) = (t + 4) * x(t + 4)

Combine like terms: 2t + 3t = 5t
(6 + 5t + t2) = (t + 4) * x(t + 4)

Reorder the terms:
6 + 5t + t2 = (4 + t) * x(t + 4)

Reorder the terms:
6 + 5t + t2 = (4 + t) * x(4 + t)

Reorder the terms for easier multiplication:
6 + 5t + t2 = x(4 + t)(4 + t)

Multiply (4 + t) * (4 + t)
6 + 5t + t2 = x(4(4 + t) + t(4 + t))
6 + 5t + t2 = x((4 * 4 + t * 4) + t(4 + t))
6 + 5t + t2 = x((16 + 4t) + t(4 + t))
6 + 5t + t2 = x(16 + 4t + (4 * t + t * t))
6 + 5t + t2 = x(16 + 4t + (4t + t2))

Combine like terms: 4t + 4t = 8t
6 + 5t + t2 = x(16 + 8t + t2)
6 + 5t + t2 = (16 * x + 8t * x + t2 * x)

Reorder the terms:
6 + 5t + t2 = (8tx + t2x + 16x)
6 + 5t + t2 = (8tx + t2x + 16x)

Solving
6 + 5t + t2 = 8tx + t2x + 16x

Solving for variable 't'.

Reorder the terms:
6 + 5t + -8tx + t2 + -1t2x + -16x = 8tx + t2x + 16x + -8tx + -1t2x + -16x

Reorder the terms:
6 + 5t + -8tx + t2 + -1t2x + -16x = 8tx + -8tx + t2x + -1t2x + 16x + -16x

Combine like terms: 8tx + -8tx = 0
6 + 5t + -8tx + t2 + -1t2x + -16x = 0 + t2x + -1t2x + 16x + -16x
6 + 5t + -8tx + t2 + -1t2x + -16x = t2x + -1t2x + 16x + -16x

Combine like terms: t2x + -1t2x = 0
6 + 5t + -8tx + t2 + -1t2x + -16x = 0 + 16x + -16x
6 + 5t + -8tx + t2 + -1t2x + -16x = 16x + -16x

Combine like terms: 16x + -16x = 0
6 + 5t + -8tx + t2 + -1t2x + -16x = 0

The solution to this equation could not be determined.