x^3+(4-h)x^2+(7-2h)x+6=0

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Solution for x^3+(4-h)x^2+(7-2h)x+6=0 equation: 


Simplifying
x3 + (4 + -1h) * x2 + (7 + -2h) * x + 6 = 0

Reorder the terms for easier multiplication:
x3 + x2(4 + -1h) + (7 + -2h) * x + 6 = 0
x3 + (4 * x2 + -1h * x2) + (7 + -2h) * x + 6 = 0

Reorder the terms:
x3 + (-1hx2 + 4x2) + (7 + -2h) * x + 6 = 0
x3 + (-1hx2 + 4x2) + (7 + -2h) * x + 6 = 0

Reorder the terms for easier multiplication:
x3 + -1hx2 + 4x2 + x(7 + -2h) + 6 = 0
x3 + -1hx2 + 4x2 + (7 * x + -2h * x) + 6 = 0

Reorder the terms:
x3 + -1hx2 + 4x2 + (-2hx + 7x) + 6 = 0
x3 + -1hx2 + 4x2 + (-2hx + 7x) + 6 = 0

Reorder the terms:
6 + -2hx + -1hx2 + 7x + 4x2 + x3 = 0

Solving
6 + -2hx + -1hx2 + 7x + 4x2 + x3 = 0

Solving for variable 'h'.

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

Add '-6' to each side of the equation.
6 + -2hx + -1hx2 + 7x + 4x2 + -6 + x3 = 0 + -6

Reorder the terms:
6 + -6 + -2hx + -1hx2 + 7x + 4x2 + x3 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -2hx + -1hx2 + 7x + 4x2 + x3 = 0 + -6
-2hx + -1hx2 + 7x + 4x2 + x3 = 0 + -6

Combine like terms: 0 + -6 = -6
-2hx + -1hx2 + 7x + 4x2 + x3 = -6

Add '-7x' to each side of the equation.
-2hx + -1hx2 + 7x + 4x2 + -7x + x3 = -6 + -7x

Reorder the terms:
-2hx + -1hx2 + 7x + -7x + 4x2 + x3 = -6 + -7x

Combine like terms: 7x + -7x = 0
-2hx + -1hx2 + 0 + 4x2 + x3 = -6 + -7x
-2hx + -1hx2 + 4x2 + x3 = -6 + -7x

Add '-4x2' to each side of the equation.
-2hx + -1hx2 + 4x2 + -4x2 + x3 = -6 + -7x + -4x2

Combine like terms: 4x2 + -4x2 = 0
-2hx + -1hx2 + 0 + x3 = -6 + -7x + -4x2
-2hx + -1hx2 + x3 = -6 + -7x + -4x2

Add '-1x3' to each side of the equation.
-2hx + -1hx2 + x3 + -1x3 = -6 + -7x + -4x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-2hx + -1hx2 + 0 = -6 + -7x + -4x2 + -1x3
-2hx + -1hx2 = -6 + -7x + -4x2 + -1x3

Reorder the terms:
6 + -2hx + -1hx2 + 7x + 4x2 + x3 = -6 + -7x + -4x2 + -1x3 + 6 + 7x + 4x2 + x3

Reorder the terms:
6 + -2hx + -1hx2 + 7x + 4x2 + x3 = -6 + 6 + -7x + 7x + -4x2 + 4x2 + -1x3 + x3

Combine like terms: -6 + 6 = 0
6 + -2hx + -1hx2 + 7x + 4x2 + x3 = 0 + -7x + 7x + -4x2 + 4x2 + -1x3 + x3
6 + -2hx + -1hx2 + 7x + 4x2 + x3 = -7x + 7x + -4x2 + 4x2 + -1x3 + x3

Combine like terms: -7x + 7x = 0
6 + -2hx + -1hx2 + 7x + 4x2 + x3 = 0 + -4x2 + 4x2 + -1x3 + x3
6 + -2hx + -1hx2 + 7x + 4x2 + x3 = -4x2 + 4x2 + -1x3 + x3

Combine like terms: -4x2 + 4x2 = 0
6 + -2hx + -1hx2 + 7x + 4x2 + x3 = 0 + -1x3 + x3
6 + -2hx + -1hx2 + 7x + 4x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
6 + -2hx + -1hx2 + 7x + 4x2 + x3 = 0

The solution to this equation could not be determined.

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