Solve y(6y+2)+5(2y+4)

Question

Simplify the expression

6 y^{2} + 12 y + 20

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2 (3 y^{2} + 6 y + 10)

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y_{1} = - 1 - \frac{21}{3} i, y_{2} = - 1 + \frac{21}{3} i

Alternative Form

y_{1} \approx - 1 - 1.527525 i, y_{2} \approx - 1 + 1.527525 i

Evaluate

y (6 y + 2) + 5 (2 y + 4)

To find the roots of the expression,set the expression equal to 0

y (6 y + 2) + 5 (2 y + 4) = 0

Calculate

More Steps

6 y^{2} + 12 y + 20 = 0

Substitute a= 6,b= 12 and c= 20 into the quadratic formula y = \frac{- b \pm b ^{2} - 4 a c}{2 a}

y = \frac{- 12 \pm 1 2 ^{2} - 4 \times 6 \times 20}{2 \times 6}

Simplify the expression

y = \frac{- 12 \pm 1 2 ^{2} - 4 \times 6 \times 20}{12}

Simplify the expression

More Steps

y = \frac{- 12 \pm - 336}{12}

Simplify the radical expression

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y = \frac{- 12 \pm 4 21 \times i}{12}

Separate the equation into 2 possible cases

y = \frac{- 12 + 4 21 \times i}{12} y = \frac{- 12 - 4 21 \times i}{12}

Simplify the expression

More Steps

y = - 1 + \frac{21}{3} i y = \frac{- 12 - 4 21 \times i}{12}

Simplify the expression

More Steps

y = - 1 + \frac{21}{3} i y = - 1 - \frac{21}{3} i

Solution

y_{1} = - 1 - \frac{21}{3} i, y_{2} = - 1 + \frac{21}{3} i

Alternative Form

y_{1} \approx - 1 - 1.527525 i, y_{2} \approx - 1 + 1.527525 i

Show Solution