4q(q-5)+14=11(2+q)

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Solution for 4q(q-5)+14=11(2+q) equation: 


Simplifying
4q(q + -5) + 14 = 11(2 + q)

Reorder the terms:
4q(-5 + q) + 14 = 11(2 + q)
(-5 * 4q + q * 4q) + 14 = 11(2 + q)
(-20q + 4q2) + 14 = 11(2 + q)

Reorder the terms:
14 + -20q + 4q2 = 11(2 + q)
14 + -20q + 4q2 = (2 * 11 + q * 11)
14 + -20q + 4q2 = (22 + 11q)

Solving
14 + -20q + 4q2 = 22 + 11q

Solving for variable 'q'.

Reorder the terms:
14 + -22 + -20q + -11q + 4q2 = 22 + 11q + -22 + -11q

Combine like terms: 14 + -22 = -8
-8 + -20q + -11q + 4q2 = 22 + 11q + -22 + -11q

Combine like terms: -20q + -11q = -31q
-8 + -31q + 4q2 = 22 + 11q + -22 + -11q

Reorder the terms:
-8 + -31q + 4q2 = 22 + -22 + 11q + -11q

Combine like terms: 22 + -22 = 0
-8 + -31q + 4q2 = 0 + 11q + -11q
-8 + -31q + 4q2 = 11q + -11q

Combine like terms: 11q + -11q = 0
-8 + -31q + 4q2 = 0

Factor a trinomial.
(-1 + -4q)(8 + -1q) = 0


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

Simplifying
-1 + -4q = 0

Solving
-1 + -4q = 0

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

Add '1' to each side of the equation.
-1 + 1 + -4q = 0 + 1

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

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

Divide each side by '-4'.
q = -0.25

Simplifying
q = -0.25

Subproblem 2
Set the factor '(8 + -1q)' equal to zero and attempt to solve:

Simplifying
8 + -1q = 0

Solving
8 + -1q = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1q = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1q = 0 + -8
-1q = 0 + -8

Combine like terms: 0 + -8 = -8
-1q = -8

Divide each side by '-1'.
q = 8

Simplifying
q = 8
Solution
q = {-0.25, 8}

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