(7t+9)(t+7)=47

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Solution for (7t+9)(t+7)=47 equation: 


Simplifying
(7t + 9)(t + 7) = 47

Reorder the terms:
(9 + 7t)(t + 7) = 47

Reorder the terms:
(9 + 7t)(7 + t) = 47

Multiply (9 + 7t) * (7 + t)
(9(7 + t) + 7t * (7 + t)) = 47
((7 * 9 + t * 9) + 7t * (7 + t)) = 47
((63 + 9t) + 7t * (7 + t)) = 47
(63 + 9t + (7 * 7t + t * 7t)) = 47
(63 + 9t + (49t + 7t2)) = 47

Combine like terms: 9t + 49t = 58t
(63 + 58t + 7t2) = 47

Solving
63 + 58t + 7t2 = 47

Solving for variable 't'.

Reorder the terms:
63 + -47 + 58t + 7t2 = 47 + -47

Combine like terms: 63 + -47 = 16
16 + 58t + 7t2 = 47 + -47

Combine like terms: 47 + -47 = 0
16 + 58t + 7t2 = 0

Factor a trinomial.
(8 + t)(2 + 7t) = 0


Subproblem 1
Set the factor '(8 + t)' equal to zero and attempt to solve:

Simplifying
8 + t = 0

Solving
8 + t = 0

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

Add '-8' to each side of the equation.
8 + -8 + t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + t = 0 + -8
t = 0 + -8

Combine like terms: 0 + -8 = -8
t = -8

Simplifying
t = -8

Subproblem 2
Set the factor '(2 + 7t)' equal to zero and attempt to solve:

Simplifying
2 + 7t = 0

Solving
2 + 7t = 0

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

Add '-2' to each side of the equation.
2 + -2 + 7t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 7t = 0 + -2
7t = 0 + -2

Combine like terms: 0 + -2 = -2
7t = -2

Divide each side by '7'.
t = -0.2857142857

Simplifying
t = -0.2857142857
Solution
t = {-8, -0.2857142857}

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