q(q-4)+1=3(q-3)

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Solution for q(q-4)+1=3(q-3) equation:


Simplifying
q(q + -4) + 1 = 3(q + -3)

Reorder the terms:
q(-4 + q) + 1 = 3(q + -3)
(-4 * q + q * q) + 1 = 3(q + -3)
(-4q + q2) + 1 = 3(q + -3)

Reorder the terms:
1 + -4q + q2 = 3(q + -3)

Reorder the terms:
1 + -4q + q2 = 3(-3 + q)
1 + -4q + q2 = (-3 * 3 + q * 3)
1 + -4q + q2 = (-9 + 3q)

Solving
1 + -4q + q2 = -9 + 3q

Solving for variable 'q'.

Reorder the terms:
1 + 9 + -4q + -3q + q2 = -9 + 3q + 9 + -3q

Combine like terms: 1 + 9 = 10
10 + -4q + -3q + q2 = -9 + 3q + 9 + -3q

Combine like terms: -4q + -3q = -7q
10 + -7q + q2 = -9 + 3q + 9 + -3q

Reorder the terms:
10 + -7q + q2 = -9 + 9 + 3q + -3q

Combine like terms: -9 + 9 = 0
10 + -7q + q2 = 0 + 3q + -3q
10 + -7q + q2 = 3q + -3q

Combine like terms: 3q + -3q = 0
10 + -7q + q2 = 0

Factor a trinomial.
(2 + -1q)(5 + -1q) = 0


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

Simplifying
2 + -1q = 0

Solving
2 + -1q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1q = 0 + -2
-1q = 0 + -2

Combine like terms: 0 + -2 = -2
-1q = -2

Divide each side by '-1'.
q = 2

Simplifying
q = 2

Subproblem 2
Set the factor '(5 + -1q)' equal to zero and attempt to solve:

Simplifying
5 + -1q = 0

Solving
5 + -1q = 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 + -1q = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1q = 0 + -5
-1q = 0 + -5

Combine like terms: 0 + -5 = -5
-1q = -5

Divide each side by '-1'.
q = 5

Simplifying
q = 5
Solution
q = {2, 5}

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