q^2(2q-5)+q^2(7q^2-4q)=

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Solution for q^2(2q-5)+q^2(7q^2-4q)= equation: 


Simplifying
q2(2q + -5) + q2(7q2 + -4q) = 0

Reorder the terms:
q2(-5 + 2q) + q2(7q2 + -4q) = 0
(-5 * q2 + 2q * q2) + q2(7q2 + -4q) = 0
(-5q2 + 2q3) + q2(7q2 + -4q) = 0

Reorder the terms:
-5q2 + 2q3 + q2(-4q + 7q2) = 0
-5q2 + 2q3 + (-4q * q2 + 7q2 * q2) = 0
-5q2 + 2q3 + (-4q3 + 7q4) = 0

Combine like terms: 2q3 + -4q3 = -2q3
-5q2 + -2q3 + 7q4 = 0

Solving
-5q2 + -2q3 + 7q4 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), 'q2'.
q2(-5 + -2q + 7q2) = 0

Factor a trinomial.
q2((-5 + -7q)(1 + -1q)) = 0


Subproblem 1
Set the factor 'q2' equal to zero and attempt to solve:

Simplifying
q2 = 0

Solving
q2 = 0

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

Simplifying
q2 = 0

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

Subproblem 2
Set the factor '(-5 + -7q)' equal to zero and attempt to solve:

Simplifying
-5 + -7q = 0

Solving
-5 + -7q = 0

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

Add '5' to each side of the equation.
-5 + 5 + -7q = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -7q = 0 + 5
-7q = 0 + 5

Combine like terms: 0 + 5 = 5
-7q = 5

Divide each side by '-7'.
q = -0.7142857143

Simplifying
q = -0.7142857143

Subproblem 3
Set the factor '(1 + -1q)' equal to zero and attempt to solve:

Simplifying
1 + -1q = 0

Solving
1 + -1q = 0

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

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

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

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

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

Simplifying
q = 1
Solution
q = {0, -0.7142857143, 1}

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