(7x+xq)(xq-4x)=

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Solution for (7x+xq)(xq-4x)= equation: 


Simplifying
(7x + xq)(xq + -4x) = 0

Reorder the terms:
(qx + 7x)(xq + -4x) = 0

Multiply (qx + 7x) * (qx + -4x)
(qx(qx + -4x) + 7x * (qx + -4x)) = 0
((qx * qx + -4x * qx) + 7x * (qx + -4x)) = 0

Reorder the terms:
((-4qx2 + q2x2) + 7x * (qx + -4x)) = 0
((-4qx2 + q2x2) + 7x * (qx + -4x)) = 0
(-4qx2 + q2x2 + (qx * 7x + -4x * 7x)) = 0
(-4qx2 + q2x2 + (7qx2 + -28x2)) = 0

Reorder the terms:
(-4qx2 + 7qx2 + q2x2 + -28x2) = 0

Combine like terms: -4qx2 + 7qx2 = 3qx2
(3qx2 + q2x2 + -28x2) = 0

Solving
3qx2 + q2x2 + -28x2 = 0

Solving for variable 'q'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(3q + q2 + -28) = 0

Factor a trinomial.
x2((q + -4)(q + 7)) = 0


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

Simplifying
x2 = 0

Solving
x2 = 0

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

Add '-1x2' to each side of the equation.
x2 + -1x2 = 0 + -1x2
Remove the zero:
0 = -1x2

Simplifying
0 = -1x2

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 '(q + -4)' equal to zero and attempt to solve:

Simplifying
q + -4 = 0

Reorder the terms:
-4 + q = 0

Solving
-4 + q = 0

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

Add '4' to each side of the equation.
-4 + 4 + q = 0 + 4

Combine like terms: -4 + 4 = 0
0 + q = 0 + 4
q = 0 + 4

Combine like terms: 0 + 4 = 4
q = 4

Simplifying
q = 4

Subproblem 3
Set the factor '(q + 7)' equal to zero and attempt to solve:

Simplifying
q + 7 = 0

Reorder the terms:
7 + q = 0

Solving
7 + q = 0

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

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

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

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

Simplifying
q = -7
Solution
q = {4, -7}

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