f(8x^2-6)=24x^2-14

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Solution for f(8x^2-6)=24x^2-14 equation: 


Simplifying
f(8x2 + -6) = 24x2 + -14

Reorder the terms:
f(-6 + 8x2) = 24x2 + -14
(-6 * f + 8x2 * f) = 24x2 + -14
(-6f + 8fx2) = 24x2 + -14

Reorder the terms:
-6f + 8fx2 = -14 + 24x2

Solving
-6f + 8fx2 = -14 + 24x2

Solving for variable 'f'.

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

Reorder the terms:
14 + -6f + 8fx2 + -24x2 = -14 + 24x2 + 14 + -24x2

Reorder the terms:
14 + -6f + 8fx2 + -24x2 = -14 + 14 + 24x2 + -24x2

Combine like terms: -14 + 14 = 0
14 + -6f + 8fx2 + -24x2 = 0 + 24x2 + -24x2
14 + -6f + 8fx2 + -24x2 = 24x2 + -24x2

Combine like terms: 24x2 + -24x2 = 0
14 + -6f + 8fx2 + -24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + -3f + 4fx2 + -12x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + -3f + 4fx2 + -12x2)' equal to zero and attempt to solve:

Simplifying
7 + -3f + 4fx2 + -12x2 = 0

Solving
7 + -3f + 4fx2 + -12x2 = 0

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

Add '-7' to each side of the equation.
7 + -3f + 4fx2 + -7 + -12x2 = 0 + -7

Reorder the terms:
7 + -7 + -3f + 4fx2 + -12x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3f + 4fx2 + -12x2 = 0 + -7
-3f + 4fx2 + -12x2 = 0 + -7

Combine like terms: 0 + -7 = -7
-3f + 4fx2 + -12x2 = -7

Add '12x2' to each side of the equation.
-3f + 4fx2 + -12x2 + 12x2 = -7 + 12x2

Combine like terms: -12x2 + 12x2 = 0
-3f + 4fx2 + 0 = -7 + 12x2
-3f + 4fx2 = -7 + 12x2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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