3q(q+4)+10=2(2q^2-7)+10q

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Solution for 3q(q+4)+10=2(2q^2-7)+10q equation: 


Simplifying
3q(q + 4) + 10 = 2(2q2 + -7) + 10q

Reorder the terms:
3q(4 + q) + 10 = 2(2q2 + -7) + 10q
(4 * 3q + q * 3q) + 10 = 2(2q2 + -7) + 10q
(12q + 3q2) + 10 = 2(2q2 + -7) + 10q

Reorder the terms:
10 + 12q + 3q2 = 2(2q2 + -7) + 10q

Reorder the terms:
10 + 12q + 3q2 = 2(-7 + 2q2) + 10q
10 + 12q + 3q2 = (-7 * 2 + 2q2 * 2) + 10q
10 + 12q + 3q2 = (-14 + 4q2) + 10q

Reorder the terms:
10 + 12q + 3q2 = -14 + 10q + 4q2

Solving
10 + 12q + 3q2 = -14 + 10q + 4q2

Solving for variable 'q'.

Reorder the terms:
10 + 14 + 12q + -10q + 3q2 + -4q2 = -14 + 10q + 4q2 + 14 + -10q + -4q2

Combine like terms: 10 + 14 = 24
24 + 12q + -10q + 3q2 + -4q2 = -14 + 10q + 4q2 + 14 + -10q + -4q2

Combine like terms: 12q + -10q = 2q
24 + 2q + 3q2 + -4q2 = -14 + 10q + 4q2 + 14 + -10q + -4q2

Combine like terms: 3q2 + -4q2 = -1q2
24 + 2q + -1q2 = -14 + 10q + 4q2 + 14 + -10q + -4q2

Reorder the terms:
24 + 2q + -1q2 = -14 + 14 + 10q + -10q + 4q2 + -4q2

Combine like terms: -14 + 14 = 0
24 + 2q + -1q2 = 0 + 10q + -10q + 4q2 + -4q2
24 + 2q + -1q2 = 10q + -10q + 4q2 + -4q2

Combine like terms: 10q + -10q = 0
24 + 2q + -1q2 = 0 + 4q2 + -4q2
24 + 2q + -1q2 = 4q2 + -4q2

Combine like terms: 4q2 + -4q2 = 0
24 + 2q + -1q2 = 0

Factor a trinomial.
(6 + -1q)(4 + q) = 0


Subproblem 1
Set the factor '(6 + -1q)' equal to zero and attempt to solve:

Simplifying
6 + -1q = 0

Solving
6 + -1q = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1q = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1q = 0 + -6
-1q = 0 + -6

Combine like terms: 0 + -6 = -6
-1q = -6

Divide each side by '-1'.
q = 6

Simplifying
q = 6

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

Simplifying
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
Solution
q = {6, -4}

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