8q(q-3)+14=-2-q(q+48)

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Solution for 8q(q-3)+14=-2-q(q+48) equation: 


Simplifying
8q(q + -3) + 14 = -2 + -1q(q + 48)

Reorder the terms:
8q(-3 + q) + 14 = -2 + -1q(q + 48)
(-3 * 8q + q * 8q) + 14 = -2 + -1q(q + 48)
(-24q + 8q2) + 14 = -2 + -1q(q + 48)

Reorder the terms:
14 + -24q + 8q2 = -2 + -1q(q + 48)

Reorder the terms:
14 + -24q + 8q2 = -2 + -1q(48 + q)
14 + -24q + 8q2 = -2 + (48 * -1q + q * -1q)
14 + -24q + 8q2 = -2 + (-48q + -1q2)

Solving
14 + -24q + 8q2 = -2 + -48q + -1q2

Solving for variable 'q'.

Reorder the terms:
14 + 2 + -24q + 48q + 8q2 + q2 = -2 + -48q + -1q2 + 2 + 48q + q2

Combine like terms: 14 + 2 = 16
16 + -24q + 48q + 8q2 + q2 = -2 + -48q + -1q2 + 2 + 48q + q2

Combine like terms: -24q + 48q = 24q
16 + 24q + 8q2 + q2 = -2 + -48q + -1q2 + 2 + 48q + q2

Combine like terms: 8q2 + q2 = 9q2
16 + 24q + 9q2 = -2 + -48q + -1q2 + 2 + 48q + q2

Reorder the terms:
16 + 24q + 9q2 = -2 + 2 + -48q + 48q + -1q2 + q2

Combine like terms: -2 + 2 = 0
16 + 24q + 9q2 = 0 + -48q + 48q + -1q2 + q2
16 + 24q + 9q2 = -48q + 48q + -1q2 + q2

Combine like terms: -48q + 48q = 0
16 + 24q + 9q2 = 0 + -1q2 + q2
16 + 24q + 9q2 = -1q2 + q2

Combine like terms: -1q2 + q2 = 0
16 + 24q + 9q2 = 0

Factor a trinomial.
(4 + 3q)(4 + 3q) = 0


Subproblem 1
Set the factor '(4 + 3q)' equal to zero and attempt to solve:

Simplifying
4 + 3q = 0

Solving
4 + 3q = 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 + 3q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3q = 0 + -4
3q = 0 + -4

Combine like terms: 0 + -4 = -4
3q = -4

Divide each side by '3'.
q = -1.333333333

Simplifying
q = -1.333333333

Subproblem 2
Set the factor '(4 + 3q)' equal to zero and attempt to solve:

Simplifying
4 + 3q = 0

Solving
4 + 3q = 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 + 3q = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3q = 0 + -4
3q = 0 + -4

Combine like terms: 0 + -4 = -4
3q = -4

Divide each side by '3'.
q = -1.333333333

Simplifying
q = -1.333333333
Solution
q = {-1.333333333, -1.333333333}

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