(3t-7)(t+19)=0

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Solution for (3t-7)(t+19)=0 equation:


Simplifying
(3t + -7)(t + 19) = 0

Reorder the terms:
(-7 + 3t)(t + 19) = 0

Reorder the terms:
(-7 + 3t)(19 + t) = 0

Multiply (-7 + 3t) * (19 + t)
(-7(19 + t) + 3t * (19 + t)) = 0
((19 * -7 + t * -7) + 3t * (19 + t)) = 0
((-133 + -7t) + 3t * (19 + t)) = 0
(-133 + -7t + (19 * 3t + t * 3t)) = 0
(-133 + -7t + (57t + 3t2)) = 0

Combine like terms: -7t + 57t = 50t
(-133 + 50t + 3t2) = 0

Solving
-133 + 50t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-19 + -1t)(7 + -3t) = 0

Subproblem 1

Set the factor '(-19 + -1t)' equal to zero and attempt to solve: Simplifying -19 + -1t = 0 Solving -19 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '19' to each side of the equation. -19 + 19 + -1t = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -1t = 0 + 19 -1t = 0 + 19 Combine like terms: 0 + 19 = 19 -1t = 19 Divide each side by '-1'. t = -19 Simplifying t = -19

Subproblem 2

Set the factor '(7 + -3t)' equal to zero and attempt to solve: Simplifying 7 + -3t = 0 Solving 7 + -3t = 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 + -3t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3t = 0 + -7 -3t = 0 + -7 Combine like terms: 0 + -7 = -7 -3t = -7 Divide each side by '-3'. t = 2.333333333 Simplifying t = 2.333333333

Solution

t = {-19, 2.333333333}

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