(f-7)(6f+7)=0

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Solution for (f-7)(6f+7)=0 equation: 


Simplifying
(f + -7)(6f + 7) = 0

Reorder the terms:
(-7 + f)(6f + 7) = 0

Reorder the terms:
(-7 + f)(7 + 6f) = 0

Multiply (-7 + f) * (7 + 6f)
(-7(7 + 6f) + f(7 + 6f)) = 0
((7 * -7 + 6f * -7) + f(7 + 6f)) = 0
((-49 + -42f) + f(7 + 6f)) = 0
(-49 + -42f + (7 * f + 6f * f)) = 0
(-49 + -42f + (7f + 6f2)) = 0

Combine like terms: -42f + 7f = -35f
(-49 + -35f + 6f2) = 0

Solving
-49 + -35f + 6f2 = 0

Solving for variable 'f'.

Factor a trinomial.
(-7 + -6f)(7 + -1f) = 0


Subproblem 1
Set the factor '(-7 + -6f)' equal to zero and attempt to solve:

Simplifying
-7 + -6f = 0

Solving
-7 + -6f = 0

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

Add '7' to each side of the equation.
-7 + 7 + -6f = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6f = 0 + 7
-6f = 0 + 7

Combine like terms: 0 + 7 = 7
-6f = 7

Divide each side by '-6'.
f = -1.166666667

Simplifying
f = -1.166666667

Subproblem 2
Set the factor '(7 + -1f)' equal to zero and attempt to solve:

Simplifying
7 + -1f = 0

Solving
7 + -1f = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1f = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1f = 0 + -7
-1f = 0 + -7

Combine like terms: 0 + -7 = -7
-1f = -7

Divide each side by '-1'.
f = 7

Simplifying
f = 7
Solution
f = {-1.166666667, 7}

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