2i+7j+(4i+5j)t=12i+9j+(2i+6j)(t-1)

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Solution for 2i+7j+(4i+5j)t=12i+9j+(2i+6j)(t-1) equation:


Simplifying
2i + 7j + (4i + 5j) * t = 12i + 9j + (2i + 6j)(t + -1)

Reorder the terms for easier multiplication:
2i + 7j + t(4i + 5j) = 12i + 9j + (2i + 6j)(t + -1)
2i + 7j + (4i * t + 5j * t) = 12i + 9j + (2i + 6j)(t + -1)
2i + 7j + (4it + 5jt) = 12i + 9j + (2i + 6j)(t + -1)

Reorder the terms:
2i + 4it + 7j + 5jt = 12i + 9j + (2i + 6j)(t + -1)

Reorder the terms:
2i + 4it + 7j + 5jt = 12i + 9j + (2i + 6j)(-1 + t)

Multiply (2i + 6j) * (-1 + t)
2i + 4it + 7j + 5jt = 12i + 9j + (2i * (-1 + t) + 6j * (-1 + t))
2i + 4it + 7j + 5jt = 12i + 9j + ((-1 * 2i + t * 2i) + 6j * (-1 + t))
2i + 4it + 7j + 5jt = 12i + 9j + ((-2i + 2it) + 6j * (-1 + t))
2i + 4it + 7j + 5jt = 12i + 9j + (-2i + 2it + (-1 * 6j + t * 6j))
2i + 4it + 7j + 5jt = 12i + 9j + (-2i + 2it + (-6j + 6jt))
2i + 4it + 7j + 5jt = 12i + 9j + (-2i + 2it + -6j + 6jt)

Reorder the terms:
2i + 4it + 7j + 5jt = 12i + -2i + 2it + 9j + -6j + 6jt

Combine like terms: 12i + -2i = 10i
2i + 4it + 7j + 5jt = 10i + 2it + 9j + -6j + 6jt

Combine like terms: 9j + -6j = 3j
2i + 4it + 7j + 5jt = 10i + 2it + 3j + 6jt

Solving
2i + 4it + 7j + 5jt = 10i + 2it + 3j + 6jt

Solving for variable 'i'.

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

Add '-10i' to each side of the equation.
2i + 4it + 7j + -10i + 5jt = 10i + 2it + 3j + -10i + 6jt

Reorder the terms:
2i + -10i + 4it + 7j + 5jt = 10i + 2it + 3j + -10i + 6jt

Combine like terms: 2i + -10i = -8i
-8i + 4it + 7j + 5jt = 10i + 2it + 3j + -10i + 6jt

Reorder the terms:
-8i + 4it + 7j + 5jt = 10i + -10i + 2it + 3j + 6jt

Combine like terms: 10i + -10i = 0
-8i + 4it + 7j + 5jt = 0 + 2it + 3j + 6jt
-8i + 4it + 7j + 5jt = 2it + 3j + 6jt

Add '-2it' to each side of the equation.
-8i + 4it + 7j + -2it + 5jt = 2it + 3j + -2it + 6jt

Reorder the terms:
-8i + 4it + -2it + 7j + 5jt = 2it + 3j + -2it + 6jt

Combine like terms: 4it + -2it = 2it
-8i + 2it + 7j + 5jt = 2it + 3j + -2it + 6jt

Reorder the terms:
-8i + 2it + 7j + 5jt = 2it + -2it + 3j + 6jt

Combine like terms: 2it + -2it = 0
-8i + 2it + 7j + 5jt = 0 + 3j + 6jt
-8i + 2it + 7j + 5jt = 3j + 6jt

Add '-7j' to each side of the equation.
-8i + 2it + 7j + -7j + 5jt = 3j + -7j + 6jt

Combine like terms: 7j + -7j = 0
-8i + 2it + 0 + 5jt = 3j + -7j + 6jt
-8i + 2it + 5jt = 3j + -7j + 6jt

Combine like terms: 3j + -7j = -4j
-8i + 2it + 5jt = -4j + 6jt

Add '-5jt' to each side of the equation.
-8i + 2it + 5jt + -5jt = -4j + 6jt + -5jt

Combine like terms: 5jt + -5jt = 0
-8i + 2it + 0 = -4j + 6jt + -5jt
-8i + 2it = -4j + 6jt + -5jt

Combine like terms: 6jt + -5jt = 1jt
-8i + 2it = -4j + 1jt

Reorder the terms:
-8i + 2it + 4j + -1jt = -4j + 4j + 1jt + -1jt

Combine like terms: -4j + 4j = 0
-8i + 2it + 4j + -1jt = 0 + 1jt + -1jt
-8i + 2it + 4j + -1jt = 1jt + -1jt

Combine like terms: 1jt + -1jt = 0
-8i + 2it + 4j + -1jt = 0

The solution to this equation could not be determined.

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