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

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


Simplifying
t(t + 7) = 4(3 + 2t)

Reorder the terms:
t(7 + t) = 4(3 + 2t)
(7 * t + t * t) = 4(3 + 2t)
(7t + t2) = 4(3 + 2t)
7t + t2 = (3 * 4 + 2t * 4)
7t + t2 = (12 + 8t)

Solving
7t + t2 = 12 + 8t

Solving for variable 't'.

Reorder the terms:
-12 + 7t + -8t + t2 = 12 + 8t + -12 + -8t

Combine like terms: 7t + -8t = -1t
-12 + -1t + t2 = 12 + 8t + -12 + -8t

Reorder the terms:
-12 + -1t + t2 = 12 + -12 + 8t + -8t

Combine like terms: 12 + -12 = 0
-12 + -1t + t2 = 0 + 8t + -8t
-12 + -1t + t2 = 8t + -8t

Combine like terms: 8t + -8t = 0
-12 + -1t + t2 = 0

Factor a trinomial.
(-3 + -1t)(4 + -1t) = 0


Subproblem 1
Set the factor '(-3 + -1t)' equal to zero and attempt to solve:

Simplifying
-3 + -1t = 0

Solving
-3 + -1t = 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 + -1t = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1t = 0 + 3
-1t = 0 + 3

Combine like terms: 0 + 3 = 3
-1t = 3

Divide each side by '-1'.
t = -3

Simplifying
t = -3

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 = {-3, 4}

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