(3t-15)(4t+22)=0

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Solution for (3t-15)(4t+22)=0 equation: 


Simplifying
(3t + -15)(4t + 22) = 0

Reorder the terms:
(-15 + 3t)(4t + 22) = 0

Reorder the terms:
(-15 + 3t)(22 + 4t) = 0

Multiply (-15 + 3t) * (22 + 4t)
(-15(22 + 4t) + 3t * (22 + 4t)) = 0
((22 * -15 + 4t * -15) + 3t * (22 + 4t)) = 0
((-330 + -60t) + 3t * (22 + 4t)) = 0
(-330 + -60t + (22 * 3t + 4t * 3t)) = 0
(-330 + -60t + (66t + 12t2)) = 0

Combine like terms: -60t + 66t = 6t
(-330 + 6t + 12t2) = 0

Solving
-330 + 6t + 12t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-55 + t + 2t2) = 0

Factor a trinomial.
6((-11 + -2t)(5 + -1t)) = 0

Ignore the factor 6.

Subproblem 1
Set the factor '(-11 + -2t)' equal to zero and attempt to solve:

Simplifying
-11 + -2t = 0

Solving
-11 + -2t = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2t = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2t = 0 + 11
-2t = 0 + 11

Combine like terms: 0 + 11 = 11
-2t = 11

Divide each side by '-2'.
t = -5.5

Simplifying
t = -5.5

Subproblem 2
Set the factor '(5 + -1t)' equal to zero and attempt to solve:

Simplifying
5 + -1t = 0

Solving
5 + -1t = 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 + -1t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1t = 0 + -5
-1t = 0 + -5

Combine like terms: 0 + -5 = -5
-1t = -5

Divide each side by '-1'.
t = 5

Simplifying
t = 5
Solution
t = {-5.5, 5}

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