(10t+7)(3t-8)=0

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Solution for (10t+7)(3t-8)=0 equation: 


Simplifying
(10t + 7)(3t + -8) = 0

Reorder the terms:
(7 + 10t)(3t + -8) = 0

Reorder the terms:
(7 + 10t)(-8 + 3t) = 0

Multiply (7 + 10t) * (-8 + 3t)
(7(-8 + 3t) + 10t * (-8 + 3t)) = 0
((-8 * 7 + 3t * 7) + 10t * (-8 + 3t)) = 0
((-56 + 21t) + 10t * (-8 + 3t)) = 0
(-56 + 21t + (-8 * 10t + 3t * 10t)) = 0
(-56 + 21t + (-80t + 30t2)) = 0

Combine like terms: 21t + -80t = -59t
(-56 + -59t + 30t2) = 0

Solving
-56 + -59t + 30t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-7 + -10t)(8 + -3t) = 0


Subproblem 1
Set the factor '(-7 + -10t)' equal to zero and attempt to solve:

Simplifying
-7 + -10t = 0

Solving
-7 + -10t = 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 + -10t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -10t = 0 + 7
-10t = 0 + 7

Combine like terms: 0 + 7 = 7
-10t = 7

Divide each side by '-10'.
t = -0.7

Simplifying
t = -0.7

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 = {-0.7, 2.666666667}

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