(q-4)(q+7)=0

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Solution for (q-4)(q+7)=0 equation: 


Simplifying
(q + -4)(q + 7) = 0

Reorder the terms:
(-4 + q)(q + 7) = 0

Reorder the terms:
(-4 + q)(7 + q) = 0

Multiply (-4 + q) * (7 + q)
(-4(7 + q) + q(7 + q)) = 0
((7 * -4 + q * -4) + q(7 + q)) = 0
((-28 + -4q) + q(7 + q)) = 0
(-28 + -4q + (7 * q + q * q)) = 0
(-28 + -4q + (7q + q2)) = 0

Combine like terms: -4q + 7q = 3q
(-28 + 3q + q2) = 0

Solving
-28 + 3q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-7 + -1q)(4 + -1q) = 0


Subproblem 1
Set the factor '(-7 + -1q)' equal to zero and attempt to solve:

Simplifying
-7 + -1q = 0

Solving
-7 + -1q = 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 + -1q = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1q = 0 + 7
-1q = 0 + 7

Combine like terms: 0 + 7 = 7
-1q = 7

Divide each side by '-1'.
q = -7

Simplifying
q = -7

Subproblem 2
Set the factor '(4 + -1q)' equal to zero and attempt to solve:

Simplifying
4 + -1q = 0

Solving
4 + -1q = 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 + -1q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1q = 0 + -4
-1q = 0 + -4

Combine like terms: 0 + -4 = -4
-1q = -4

Divide each side by '-1'.
q = 4

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

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