Final answer:
To solve 7-57m=-8m², set the equation to zero and factor it. The solutions to 8m² + 57m - 7 = 0 are m = -1/8 and m = -7 by factoring and solving the resulting linear equations.
Step-by-step explanation:
To solve the quadratic equation 7-57m=-8m² by factoring, begin by moving all terms to one side of the equation to set the equation to zero.
First, add 8m² to both sides:
8m² + 57m - 7 = 0
Now factor the quadratic equation. We look for two numbers that multiply to 8*(-7) = -56 and add to 57. These numbers are +56 and +1. We rewrite the middle term using these two numbers:
8m² + 56m + m - 7 = 0
Factor by grouping:
8m(m + 7) + 1(m + 7) = 0
(8m + 1)(m + 7) = 0
Now set each factor equal to zero and solve for m:
8m + 1 = 0 ⇒ m = -1/8
m + 7 = 0 ⇒ m = -7
Therefore, the solution to the quadratic equation is m = -1/8 or m = -7.