4t(2t+6)+7t(3t+5)=

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Solution for 4t(2t+6)+7t(3t+5)= equation:


Simplifying
4t(2t + 6) + 7t(3t + 5) = 0

Reorder the terms:
4t(6 + 2t) + 7t(3t + 5) = 0
(6 * 4t + 2t * 4t) + 7t(3t + 5) = 0
(24t + 8t2) + 7t(3t + 5) = 0

Reorder the terms:
24t + 8t2 + 7t(5 + 3t) = 0
24t + 8t2 + (5 * 7t + 3t * 7t) = 0
24t + 8t2 + (35t + 21t2) = 0

Reorder the terms:
24t + 35t + 8t2 + 21t2 = 0

Combine like terms: 24t + 35t = 59t
59t + 8t2 + 21t2 = 0

Combine like terms: 8t2 + 21t2 = 29t2
59t + 29t2 = 0

Solving
59t + 29t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), 't'.
t(59 + 29t) = 0

Subproblem 1

Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0

Subproblem 2

Set the factor '(59 + 29t)' equal to zero and attempt to solve: Simplifying 59 + 29t = 0 Solving 59 + 29t = 0 Move all terms containing t to the left, all other terms to the right. Add '-59' to each side of the equation. 59 + -59 + 29t = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 29t = 0 + -59 29t = 0 + -59 Combine like terms: 0 + -59 = -59 29t = -59 Divide each side by '29'. t = -2.034482759 Simplifying t = -2.034482759

Solution

t = {0, -2.034482759}

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