4f(f+3)+5=17+4f

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Solution for 4f(f+3)+5=17+4f equation: 


Simplifying
4f(f + 3) + 5 = 17 + 4f

Reorder the terms:
4f(3 + f) + 5 = 17 + 4f
(3 * 4f + f * 4f) + 5 = 17 + 4f
(12f + 4f2) + 5 = 17 + 4f

Reorder the terms:
5 + 12f + 4f2 = 17 + 4f

Solving
5 + 12f + 4f2 = 17 + 4f

Solving for variable 'f'.

Reorder the terms:
5 + -17 + 12f + -4f + 4f2 = 17 + 4f + -17 + -4f

Combine like terms: 5 + -17 = -12
-12 + 12f + -4f + 4f2 = 17 + 4f + -17 + -4f

Combine like terms: 12f + -4f = 8f
-12 + 8f + 4f2 = 17 + 4f + -17 + -4f

Reorder the terms:
-12 + 8f + 4f2 = 17 + -17 + 4f + -4f

Combine like terms: 17 + -17 = 0
-12 + 8f + 4f2 = 0 + 4f + -4f
-12 + 8f + 4f2 = 4f + -4f

Combine like terms: 4f + -4f = 0
-12 + 8f + 4f2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 2f + f2) = 0

Factor a trinomial.
4((-3 + -1f)(1 + -1f)) = 0

Ignore the factor 4.

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

Simplifying
-3 + -1f = 0

Solving
-3 + -1f = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1f = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1f = 0 + 3
-1f = 0 + 3

Combine like terms: 0 + 3 = 3
-1f = 3

Divide each side by '-1'.
f = -3

Simplifying
f = -3

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

Simplifying
1 + -1f = 0

Solving
1 + -1f = 0

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

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

Combine like terms: 1 + -1 = 0
0 + -1f = 0 + -1
-1f = 0 + -1

Combine like terms: 0 + -1 = -1
-1f = -1

Divide each side by '-1'.
f = 1

Simplifying
f = 1
Solution
f = {-3, 1}

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