4t^2-9t+16=15-4t

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Solution for 4t^2-9t+16=15-4t equation: 


Simplifying
4t2 + -9t + 16 = 15 + -4t

Reorder the terms:
16 + -9t + 4t2 = 15 + -4t

Solving
16 + -9t + 4t2 = 15 + -4t

Solving for variable 't'.

Reorder the terms:
16 + -15 + -9t + 4t + 4t2 = 15 + -4t + -15 + 4t

Combine like terms: 16 + -15 = 1
1 + -9t + 4t + 4t2 = 15 + -4t + -15 + 4t

Combine like terms: -9t + 4t = -5t
1 + -5t + 4t2 = 15 + -4t + -15 + 4t

Reorder the terms:
1 + -5t + 4t2 = 15 + -15 + -4t + 4t

Combine like terms: 15 + -15 = 0
1 + -5t + 4t2 = 0 + -4t + 4t
1 + -5t + 4t2 = -4t + 4t

Combine like terms: -4t + 4t = 0
1 + -5t + 4t2 = 0

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


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

Simplifying
1 + -4t = 0

Solving
1 + -4t = 0

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

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

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

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

Divide each side by '-4'.
t = 0.25

Simplifying
t = 0.25

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

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

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

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

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

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

Simplifying
t = 1
Solution
t = {0.25, 1}

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