What are the solutions to the equation factor 6t(t+3)=t-5 ?

The solutions to the equation factor 6t(t+3)=t-5 are t=-1/3 ,t=-5/2

Find the zeros of factor 6t(t+3)=t-5

The zeros of factor 6t(t+3)=t-5 are t=-1/3 ,t=-5/2

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6 t (t + 3) = t - 5

t = - \frac{1}{3}, t = - \frac{5}{2}

Decimal Notation

t = - 0.33333 \dots, t = - 2.5

Solution steps

6 t (t + 3) = t - 5

Expand

6 t (t + 3) : 6 t^{2} + 18 t

6 t^{2} + 18 t = t - 5

Move

5

to the left side

6 t^{2} + 18 t + 5 = t

Move

t

to the left side

6 t^{2} + 17 t + 5 = 0

Factor

6 t^{2} + 17 t + 5 : (3 t + 1) (2 t + 5)

(3 t + 1) (2 t + 5) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

3 t + 1 = 0 or 2 t + 5 = 0

Solve

3 t + 1 = 0 : t = - \frac{1}{3}

Solve

2 t + 5 = 0 : t = - \frac{5}{2}

The solutions to the quadratic equation are:

t = - \frac{1}{3}, t = - \frac{5}{2}

16 (5 - 2 x)^{2} + 33 = 42

- s^{2} - 2 s + 5 = 0

y, 40 x^{2} + 3 y^{2} - 7 x + y + 1 = 0

t^{2} + 6 t - 4 = 0

x^{2} + 6 x + 19 = 4 x

What are the solutions to the equation factor 6t(t+3)=t-5 ?
The solutions to the equation factor 6t(t+3)=t-5 are t=-1/3 ,t=-5/2
Find the zeros of factor 6t(t+3)=t-5
The zeros of factor 6t(t+3)=t-5 are t=-1/3 ,t=-5/2