4t^2-9t+16=15-14t^2

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Solution for 4t^2-9t+16=15-14t^2 equation: 


Simplifying
4t2 + -9t + 16 = 15 + -14t2

Reorder the terms:
16 + -9t + 4t2 = 15 + -14t2

Solving
16 + -9t + 4t2 = 15 + -14t2

Solving for variable 't'.

Reorder the terms:
16 + -15 + -9t + 4t2 + 14t2 = 15 + -14t2 + -15 + 14t2

Combine like terms: 16 + -15 = 1
1 + -9t + 4t2 + 14t2 = 15 + -14t2 + -15 + 14t2

Combine like terms: 4t2 + 14t2 = 18t2
1 + -9t + 18t2 = 15 + -14t2 + -15 + 14t2

Reorder the terms:
1 + -9t + 18t2 = 15 + -15 + -14t2 + 14t2

Combine like terms: 15 + -15 = 0
1 + -9t + 18t2 = 0 + -14t2 + 14t2
1 + -9t + 18t2 = -14t2 + 14t2

Combine like terms: -14t2 + 14t2 = 0
1 + -9t + 18t2 = 0

Factor a trinomial.
(1 + -6t)(1 + -3t) = 0


Subproblem 1
Set the factor '(1 + -6t)' equal to zero and attempt to solve:

Simplifying
1 + -6t = 0

Solving
1 + -6t = 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 + -6t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6t = 0 + -1
-6t = 0 + -1

Combine like terms: 0 + -1 = -1
-6t = -1

Divide each side by '-6'.
t = 0.1666666667

Simplifying
t = 0.1666666667

Subproblem 2
Set the factor '(1 + -3t)' equal to zero and attempt to solve:

Simplifying
1 + -3t = 0

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

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

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

Divide each side by '-3'.
t = 0.3333333333

Simplifying
t = 0.3333333333
Solution
t = {0.1666666667, 0.3333333333}

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