Question

Solve the equation 4y^2 + 5y - 21 = 0

Answer 1

Answer:

Step-by-step explanation:

Simplifying

4y2 + 5y + -21 = 0

Reorder the terms:

-21 + 5y + 4y2 = 0

Solving

-21 + 5y + 4y2 = 0

Solving for variable 'y'.

Factor a trinomial.

(-3 + -1y)(7 + -4y) = 0

Subproblem 1

Set the factor '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying

-3 + -1y = 0

Solving

-3 + -1y = 0

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

Add '3' to each side of the equation.

-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0

0 + -1y = 0 + 3

-1y = 0 + 3

Combine like terms: 0 + 3 = 3

-1y = 3

Divide each side by '-1'.

y = -3

Simplifying

y = -3

Subproblem 2

Set the factor '(7 + -4y)' equal to zero and attempt to solve:

Simplifying

7 + -4y = 0

Solving

7 + -4y = 0

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

Add '-7' to each side of the equation.

7 + -7 + -4y = 0 + -7

Combine like terms: 7 + -7 = 0

0 + -4y = 0 + -7

-4y = 0 + -7

Combine like terms: 0 + -7 = -7

-4y = -7

Divide each side by '-4'.

y = 1.75

Simplifying

y = 1.75

Solution

y = {-3, 1.75}

Answer 2

Answer:

(y+3)(y-7/4)=0

Step-by-step explanation:

4y²+5y-21=0

a=4

b=5

c=-21

-b±$\sqrt{b^{2}-4ac }$/2a

-5±$\sqrt{5^{2}-4(4)(-21) }$/2(4)

-5±$\sqrt{25^{2}-(-336) }$/2(4)

-5±$\sqrt{25+336}$/2(4)

-5±√361/2(4)

-5±19/8

(-5+19)/8=14/8=7/4

(-5-19)/8=-24/8=-3

(y+3)(y-7/4)=0