(4t-1)(t+5)=-26

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Solution for (4t-1)(t+5)=-26 equation:


Simplifying
(4t + -1)(t + 5) = -26

Reorder the terms:
(-1 + 4t)(t + 5) = -26

Reorder the terms:
(-1 + 4t)(5 + t) = -26

Multiply (-1 + 4t) * (5 + t)
(-1(5 + t) + 4t * (5 + t)) = -26
((5 * -1 + t * -1) + 4t * (5 + t)) = -26
((-5 + -1t) + 4t * (5 + t)) = -26
(-5 + -1t + (5 * 4t + t * 4t)) = -26
(-5 + -1t + (20t + 4t2)) = -26

Combine like terms: -1t + 20t = 19t
(-5 + 19t + 4t2) = -26

Solving
-5 + 19t + 4t2 = -26

Solving for variable 't'.

Reorder the terms:
-5 + 26 + 19t + 4t2 = -26 + 26

Combine like terms: -5 + 26 = 21
21 + 19t + 4t2 = -26 + 26

Combine like terms: -26 + 26 = 0
21 + 19t + 4t2 = 0

Factor a trinomial.
(3 + t)(7 + 4t) = 0

Subproblem 1

Set the factor '(3 + t)' equal to zero and attempt to solve: Simplifying 3 + t = 0 Solving 3 + t = 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 + t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + t = 0 + -3 t = 0 + -3 Combine like terms: 0 + -3 = -3 t = -3 Simplifying t = -3

Subproblem 2

Set the factor '(7 + 4t)' equal to zero and attempt to solve: Simplifying 7 + 4t = 0 Solving 7 + 4t = 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 + 4t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 4t = 0 + -7 4t = 0 + -7 Combine like terms: 0 + -7 = -7 4t = -7 Divide each side by '4'. t = -1.75 Simplifying t = -1.75

Solution

t = {-3, -1.75}

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