(13t+7)(6t-18)=0

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Solution for (13t+7)(6t-18)=0 equation: 


Simplifying
(13t + 7)(6t + -18) = 0

Reorder the terms:
(7 + 13t)(6t + -18) = 0

Reorder the terms:
(7 + 13t)(-18 + 6t) = 0

Multiply (7 + 13t) * (-18 + 6t)
(7(-18 + 6t) + 13t * (-18 + 6t)) = 0
((-18 * 7 + 6t * 7) + 13t * (-18 + 6t)) = 0
((-126 + 42t) + 13t * (-18 + 6t)) = 0
(-126 + 42t + (-18 * 13t + 6t * 13t)) = 0
(-126 + 42t + (-234t + 78t2)) = 0

Combine like terms: 42t + -234t = -192t
(-126 + -192t + 78t2) = 0

Solving
-126 + -192t + 78t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-21 + -32t + 13t2) = 0

Factor a trinomial.
6((-7 + -13t)(3 + -1t)) = 0

Ignore the factor 6.

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 '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-0.5384615385, 3}

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