(12t+7)(5t-15)=0

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Solution for (12t+7)(5t-15)=0 equation: 


Simplifying
(12t + 7)(5t + -15) = 0

Reorder the terms:
(7 + 12t)(5t + -15) = 0

Reorder the terms:
(7 + 12t)(-15 + 5t) = 0

Multiply (7 + 12t) * (-15 + 5t)
(7(-15 + 5t) + 12t * (-15 + 5t)) = 0
((-15 * 7 + 5t * 7) + 12t * (-15 + 5t)) = 0
((-105 + 35t) + 12t * (-15 + 5t)) = 0
(-105 + 35t + (-15 * 12t + 5t * 12t)) = 0
(-105 + 35t + (-180t + 60t2)) = 0

Combine like terms: 35t + -180t = -145t
(-105 + -145t + 60t2) = 0

Solving
-105 + -145t + 60t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-21 + -29t + 12t2) = 0

Factor a trinomial.
5((-7 + -12t)(3 + -1t)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-7 + -12t)' equal to zero and attempt to solve:

Simplifying
-7 + -12t = 0

Solving
-7 + -12t = 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 + -12t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -12t = 0 + 7
-12t = 0 + 7

Combine like terms: 0 + 7 = 7
-12t = 7

Divide each side by '-12'.
t = -0.5833333333

Simplifying
t = -0.5833333333

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 = {-0.5833333333, 3}

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