(7t+1)(5t+8)=162

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Solution for (7t+1)(5t+8)=162 equation: 


Simplifying
(7t + 1)(5t + 8) = 162

Reorder the terms:
(1 + 7t)(5t + 8) = 162

Reorder the terms:
(1 + 7t)(8 + 5t) = 162

Multiply (1 + 7t) * (8 + 5t)
(1(8 + 5t) + 7t * (8 + 5t)) = 162
((8 * 1 + 5t * 1) + 7t * (8 + 5t)) = 162
((8 + 5t) + 7t * (8 + 5t)) = 162
(8 + 5t + (8 * 7t + 5t * 7t)) = 162
(8 + 5t + (56t + 35t2)) = 162

Combine like terms: 5t + 56t = 61t
(8 + 61t + 35t2) = 162

Solving
8 + 61t + 35t2 = 162

Solving for variable 't'.

Reorder the terms:
8 + -162 + 61t + 35t2 = 162 + -162

Combine like terms: 8 + -162 = -154
-154 + 61t + 35t2 = 162 + -162

Combine like terms: 162 + -162 = 0
-154 + 61t + 35t2 = 0

Factor a trinomial.
(-22 + -7t)(7 + -5t) = 0


Subproblem 1
Set the factor '(-22 + -7t)' equal to zero and attempt to solve:

Simplifying
-22 + -7t = 0

Solving
-22 + -7t = 0

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

Add '22' to each side of the equation.
-22 + 22 + -7t = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -7t = 0 + 22
-7t = 0 + 22

Combine like terms: 0 + 22 = 22
-7t = 22

Divide each side by '-7'.
t = -3.142857143

Simplifying
t = -3.142857143

Subproblem 2
Set the factor '(7 + -5t)' equal to zero and attempt to solve:

Simplifying
7 + -5t = 0

Solving
7 + -5t = 0

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

Add '-7' to each side of the equation.
7 + -7 + -5t = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -5t = 0 + -7
-5t = 0 + -7

Combine like terms: 0 + -7 = -7
-5t = -7

Divide each side by '-5'.
t = 1.4

Simplifying
t = 1.4
Solution
t = {-3.142857143, 1.4}

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