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

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


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

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

Combine like terms: -9 + 16 = 7
7 + 4t2 = 15 + -4t

Solving
7 + 4t2 = 15 + -4t

Solving for variable 't'.

Reorder the terms:
7 + -15 + 4t + 4t2 = 15 + -4t + -15 + 4t

Combine like terms: 7 + -15 = -8
-8 + 4t + 4t2 = 15 + -4t + -15 + 4t

Reorder the terms:
-8 + 4t + 4t2 = 15 + -15 + -4t + 4t

Combine like terms: 15 + -15 = 0
-8 + 4t + 4t2 = 0 + -4t + 4t
-8 + 4t + 4t2 = -4t + 4t

Combine like terms: -4t + 4t = 0
-8 + 4t + 4t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-2 + t + t2) = 0

Factor a trinomial.
4((-2 + -1t)(1 + -1t)) = 0

Ignore the factor 4.

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

Simplifying
-2 + -1t = 0

Solving
-2 + -1t = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1t = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1t = 0 + 2
-1t = 0 + 2

Combine like terms: 0 + 2 = 2
-1t = 2

Divide each side by '-1'.
t = -2

Simplifying
t = -2

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 = {-2, 1}

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