37t^2+16=t(48+t)

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Solution for 37t^2+16=t(48+t) equation: 


Simplifying
37t2 + 16 = t(48 + t)

Reorder the terms:
16 + 37t2 = t(48 + t)
16 + 37t2 = (48 * t + t * t)
16 + 37t2 = (48t + t2)

Solving
16 + 37t2 = 48t + t2

Solving for variable 't'.

Reorder the terms:
16 + -48t + 37t2 + -1t2 = 48t + t2 + -48t + -1t2

Combine like terms: 37t2 + -1t2 = 36t2
16 + -48t + 36t2 = 48t + t2 + -48t + -1t2

Reorder the terms:
16 + -48t + 36t2 = 48t + -48t + t2 + -1t2

Combine like terms: 48t + -48t = 0
16 + -48t + 36t2 = 0 + t2 + -1t2
16 + -48t + 36t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
16 + -48t + 36t2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(4 + -12t + 9t2) = 0

Factor a trinomial.
4((2 + -3t)(2 + -3t)) = 0

Ignore the factor 4.

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

Simplifying
2 + -3t = 0

Solving
2 + -3t = 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 + -3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3t = 0 + -2
-3t = 0 + -2

Combine like terms: 0 + -2 = -2
-3t = -2

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667

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

Simplifying
2 + -3t = 0

Solving
2 + -3t = 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 + -3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3t = 0 + -2
-3t = 0 + -2

Combine like terms: 0 + -2 = -2
-3t = -2

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667
Solution
t = {0.6666666667, 0.6666666667}

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