t(11+t)=4(2t+7)

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Solution for t(11+t)=4(2t+7) equation: 


Simplifying
t(11 + t) = 4(2t + 7)
(11 * t + t * t) = 4(2t + 7)
(11t + t2) = 4(2t + 7)

Reorder the terms:
11t + t2 = 4(7 + 2t)
11t + t2 = (7 * 4 + 2t * 4)
11t + t2 = (28 + 8t)

Solving
11t + t2 = 28 + 8t

Solving for variable 't'.

Reorder the terms:
-28 + 11t + -8t + t2 = 28 + 8t + -28 + -8t

Combine like terms: 11t + -8t = 3t
-28 + 3t + t2 = 28 + 8t + -28 + -8t

Reorder the terms:
-28 + 3t + t2 = 28 + -28 + 8t + -8t

Combine like terms: 28 + -28 = 0
-28 + 3t + t2 = 0 + 8t + -8t
-28 + 3t + t2 = 8t + -8t

Combine like terms: 8t + -8t = 0
-28 + 3t + t2 = 0

Factor a trinomial.
(-7 + -1t)(4 + -1t) = 0


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

Simplifying
-7 + -1t = 0

Solving
-7 + -1t = 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 + -1t = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1t = 0 + 7
-1t = 0 + 7

Combine like terms: 0 + 7 = 7
-1t = 7

Divide each side by '-1'.
t = -7

Simplifying
t = -7

Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-7, 4}

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