12x^5=4x^7+8x^6

Solution for 12x^5=4x^7+8x^6 equation:

Simplifying
12x5 = 4x7 + 8x6

Reorder the terms:
12x5 = 8x6 + 4x7

Solving
12x5 = 8x6 + 4x7

Solving for variable 'x'.

Reorder the terms:
12x5 + -8x6 + -4x7 = 8x6 + -8x6 + 4x7 + -4x7

Combine like terms: 8x6 + -8x6 = 0
12x5 + -8x6 + -4x7 = 0 + 4x7 + -4x7
12x5 + -8x6 + -4x7 = 4x7 + -4x7

Combine like terms: 4x7 + -4x7 = 0
12x5 + -8x6 + -4x7 = 0

Factor out the Greatest Common Factor (GCF), '4x5'.
4x5(3 + -2x + -1x2) = 0

Factor a trinomial.
4x5((1 + -1x)(3 + x)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x5' equal to zero and attempt to solve:

Simplifying
x5 = 0

Solving
x5 = 0

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

Simplifying
x5 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 3
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {1, -3}