(13t+7)(6t-8)=0

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Solution for (13t+7)(6t-8)=0 equation: 


Simplifying
(13t + 7)(6t + -8) = 0

Reorder the terms:
(7 + 13t)(6t + -8) = 0

Reorder the terms:
(7 + 13t)(-8 + 6t) = 0

Multiply (7 + 13t) * (-8 + 6t)
(7(-8 + 6t) + 13t * (-8 + 6t)) = 0
((-8 * 7 + 6t * 7) + 13t * (-8 + 6t)) = 0
((-56 + 42t) + 13t * (-8 + 6t)) = 0
(-56 + 42t + (-8 * 13t + 6t * 13t)) = 0
(-56 + 42t + (-104t + 78t2)) = 0

Combine like terms: 42t + -104t = -62t
(-56 + -62t + 78t2) = 0

Solving
-56 + -62t + 78t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-28 + -31t + 39t2) = 0

Factor a trinomial.
2((-7 + -13t)(4 + -3t)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-7 + -13t)' equal to zero and attempt to solve:

Simplifying
-7 + -13t = 0

Solving
-7 + -13t = 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 + -13t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -13t = 0 + 7
-13t = 0 + 7

Combine like terms: 0 + 7 = 7
-13t = 7

Divide each side by '-13'.
t = -0.5384615385

Simplifying
t = -0.5384615385

Subproblem 2
Set the factor '(4 + -3t)' equal to zero and attempt to solve:

Simplifying
4 + -3t = 0

Solving
4 + -3t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3t = 0 + -4
-3t = 0 + -4

Combine like terms: 0 + -4 = -4
-3t = -4

Divide each side by '-3'.
t = 1.333333333

Simplifying
t = 1.333333333
Solution
t = {-0.5384615385, 1.333333333}

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