(13t+7)(6t+-5)=0

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Solution for (13t+7)(6t+-5)=0 equation: 


Simplifying
(13t + 7)(6t + -5) = 0

Reorder the terms:
(7 + 13t)(6t + -5) = 0

Reorder the terms:
(7 + 13t)(-5 + 6t) = 0

Multiply (7 + 13t) * (-5 + 6t)
(7(-5 + 6t) + 13t * (-5 + 6t)) = 0
((-5 * 7 + 6t * 7) + 13t * (-5 + 6t)) = 0
((-35 + 42t) + 13t * (-5 + 6t)) = 0
(-35 + 42t + (-5 * 13t + 6t * 13t)) = 0
(-35 + 42t + (-65t + 78t2)) = 0

Combine like terms: 42t + -65t = -23t
(-35 + -23t + 78t2) = 0

Solving
-35 + -23t + 78t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-7 + -13t)(5 + -6t) = 0


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 '(5 + -6t)' equal to zero and attempt to solve:

Simplifying
5 + -6t = 0

Solving
5 + -6t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6t = 0 + -5
-6t = 0 + -5

Combine like terms: 0 + -5 = -5
-6t = -5

Divide each side by '-6'.
t = 0.8333333333

Simplifying
t = 0.8333333333
Solution
t = {-0.5384615385, 0.8333333333}

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