(q-4)(q-7)=

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Solution for (q-4)(q-7)= 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 = -11q
(28 + -11q + q2) = 0

Solving
28 + -11q + q2 = 0

Solving for variable 'q'.

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


Subproblem 1
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

Subproblem 2
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
Solution
q = {4, 7}

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