(4j-5k)*(5i+5j+7k)=equation

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Solution for (4j-5k)*(5i+5j+7k)=equation equation: 


Simplifying
(4j + -5k)(5i + 5j + 7k) = equation

Multiply (4j + -5k) * (5i + 5j + 7k)
(4j * (5i + 5j + 7k) + -5k * (5i + 5j + 7k)) = equation
((5i * 4j + 5j * 4j + 7k * 4j) + -5k * (5i + 5j + 7k)) = equation

Reorder the terms:
((20ij + 28jk + 20j2) + -5k * (5i + 5j + 7k)) = equation
((20ij + 28jk + 20j2) + -5k * (5i + 5j + 7k)) = equation
(20ij + 28jk + 20j2 + (5i * -5k + 5j * -5k + 7k * -5k)) = equation
(20ij + 28jk + 20j2 + (-25ik + -25jk + -35k2)) = equation

Reorder the terms:
(20ij + -25ik + 28jk + -25jk + 20j2 + -35k2) = equation

Combine like terms: 28jk + -25jk = 3jk
(20ij + -25ik + 3jk + 20j2 + -35k2) = equation

Solving
20ij + -25ik + 3jk + 20j2 + -35k2 = aeinoqtu

Solving for variable 'i'.

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

Add '-1aeinoqtu' to each side of the equation.
20ij + -25ik + 3jk + 20j2 + -1aeinoqtu + -35k2 = aeinoqtu + -1aeinoqtu

Reorder the terms:
-1aeinoqtu + 20ij + -25ik + 3jk + 20j2 + -35k2 = aeinoqtu + -1aeinoqtu

Combine like terms: aeinoqtu + -1aeinoqtu = 0
-1aeinoqtu + 20ij + -25ik + 3jk + 20j2 + -35k2 = 0

Add '-3jk' to each side of the equation.
-1aeinoqtu + 20ij + -25ik + 3jk + 20j2 + -3jk + -35k2 = 0 + -3jk

Reorder the terms:
-1aeinoqtu + 20ij + -25ik + 3jk + -3jk + 20j2 + -35k2 = 0 + -3jk

Combine like terms: 3jk + -3jk = 0
-1aeinoqtu + 20ij + -25ik + 0 + 20j2 + -35k2 = 0 + -3jk
-1aeinoqtu + 20ij + -25ik + 20j2 + -35k2 = 0 + -3jk
Remove the zero:
-1aeinoqtu + 20ij + -25ik + 20j2 + -35k2 = -3jk

Add '-20j2' to each side of the equation.
-1aeinoqtu + 20ij + -25ik + 20j2 + -20j2 + -35k2 = -3jk + -20j2

Combine like terms: 20j2 + -20j2 = 0
-1aeinoqtu + 20ij + -25ik + 0 + -35k2 = -3jk + -20j2
-1aeinoqtu + 20ij + -25ik + -35k2 = -3jk + -20j2

Add '35k2' to each side of the equation.
-1aeinoqtu + 20ij + -25ik + -35k2 + 35k2 = -3jk + -20j2 + 35k2

Combine like terms: -35k2 + 35k2 = 0
-1aeinoqtu + 20ij + -25ik + 0 = -3jk + -20j2 + 35k2
-1aeinoqtu + 20ij + -25ik = -3jk + -20j2 + 35k2

Reorder the terms:
-1aeinoqtu + 20ij + -25ik + 3jk + 20j2 + -35k2 = -3jk + 3jk + -20j2 + 20j2 + 35k2 + -35k2

Combine like terms: -3jk + 3jk = 0
-1aeinoqtu + 20ij + -25ik + 3jk + 20j2 + -35k2 = 0 + -20j2 + 20j2 + 35k2 + -35k2
-1aeinoqtu + 20ij + -25ik + 3jk + 20j2 + -35k2 = -20j2 + 20j2 + 35k2 + -35k2

Combine like terms: -20j2 + 20j2 = 0
-1aeinoqtu + 20ij + -25ik + 3jk + 20j2 + -35k2 = 0 + 35k2 + -35k2
-1aeinoqtu + 20ij + -25ik + 3jk + 20j2 + -35k2 = 35k2 + -35k2

Combine like terms: 35k2 + -35k2 = 0
-1aeinoqtu + 20ij + -25ik + 3jk + 20j2 + -35k2 = 0

The solution to this equation could not be determined.

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