-7x^2=2x^4-9x^3

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Solution for -7x^2=2x^4-9x^3 equation: 


Simplifying
-7x2 = 2x4 + -9x3

Reorder the terms:
-7x2 = -9x3 + 2x4

Solving
-7x2 = -9x3 + 2x4

Solving for variable 'x'.

Reorder the terms:
-7x2 + 9x3 + -2x4 = -9x3 + 9x3 + 2x4 + -2x4

Combine like terms: -9x3 + 9x3 = 0
-7x2 + 9x3 + -2x4 = 0 + 2x4 + -2x4
-7x2 + 9x3 + -2x4 = 2x4 + -2x4

Combine like terms: 2x4 + -2x4 = 0
-7x2 + 9x3 + -2x4 = 0

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-7 + 9x + -2x2) = 0

Factor a trinomial.
x2((-7 + 2x)(1 + -1x)) = 0


Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

Subproblem 2
Set the factor '(-7 + 2x)' equal to zero and attempt to solve:

Simplifying
-7 + 2x = 0

Solving
-7 + 2x = 0

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

Add '7' to each side of the equation.
-7 + 7 + 2x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + 2x = 0 + 7
2x = 0 + 7

Combine like terms: 0 + 7 = 7
2x = 7

Divide each side by '2'.
x = 3.5

Simplifying
x = 3.5

Subproblem 3
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
Solution
x = {0, 3.5, 1}

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