Use the zero product property to find the solutions to the equation 6x^2 - 5x = 56.

x = - 8 or x = 7/6

x = -8/3 or x = 7/2

x = -1/2 or x = 56/3

x = - 3/7 or x = 2/3

Step-by-step explanation:

solving for x

6x²-5x=56

subtract 56 from both sides

6x²-5x-56=0

using middle term break method

factorise (56) (6) = (2*2*2*7) (2*3)

= (2*2*2*2) makes 16 and combining (3*7) makes 21

so we have

=6x²+16x-21x-56=0

taking factors out of first two terms and then other two terms

=>2x (3x+8) - 7 (3x+8) = 0

=> (2x-7) (3x+8) = 0

either 2x-7=0 or 3x+8=0

2x=7 or 3x=-8

x=7/2 or x=-8/3

x = 7/2 or x = - 8/3

Step-by-step explanation:

Solve for x over the real numbers:

6 x^2 - 5 x = 56

Divide both sides by 6:

x^2 - (5 x) / 6 = 28/3

Add 25/144 to both sides:

x^2 - (5 x) / 6 + 25/144 = 1369/144

Write the left hand side as a square:

(x - 5/12) ^2 = 1369/144

Take the square root of both sides:

x - 5/12 = 37/12 or x - 5/12 = - 37/12

Add 5/12 to both sides:

x = 7/2 or x - 5/12 = - 37/12

Add 5/12 to both sides:

Answer: x = 7/2 or x = - 8/3