(7t+8)(3t-8)=0

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Solution for (7t+8)(3t-8)=0 equation: 


Simplifying
(7t + 8)(3t + -8) = 0

Reorder the terms:
(8 + 7t)(3t + -8) = 0

Reorder the terms:
(8 + 7t)(-8 + 3t) = 0

Multiply (8 + 7t) * (-8 + 3t)
(8(-8 + 3t) + 7t * (-8 + 3t)) = 0
((-8 * 8 + 3t * 8) + 7t * (-8 + 3t)) = 0
((-64 + 24t) + 7t * (-8 + 3t)) = 0
(-64 + 24t + (-8 * 7t + 3t * 7t)) = 0
(-64 + 24t + (-56t + 21t2)) = 0

Combine like terms: 24t + -56t = -32t
(-64 + -32t + 21t2) = 0

Solving
-64 + -32t + 21t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-8 + -7t)(8 + -3t) = 0


Subproblem 1
Set the factor '(-8 + -7t)' equal to zero and attempt to solve:

Simplifying
-8 + -7t = 0

Solving
-8 + -7t = 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 + -7t = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -7t = 0 + 8
-7t = 0 + 8

Combine like terms: 0 + 8 = 8
-7t = 8

Divide each side by '-7'.
t = -1.142857143

Simplifying
t = -1.142857143

Subproblem 2
Set the factor '(8 + -3t)' equal to zero and attempt to solve:

Simplifying
8 + -3t = 0

Solving
8 + -3t = 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 + -3t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3t = 0 + -8
-3t = 0 + -8

Combine like terms: 0 + -8 = -8
-3t = -8

Divide each side by '-3'.
t = 2.666666667

Simplifying
t = 2.666666667
Solution
t = {-1.142857143, 2.666666667}

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