=(4m-1)(m+2)

Solution for =(4m-1)(m+2) equation:

Simplifying
0 = (4m + -1)(m + 2)

Reorder the terms:
0 = (-1 + 4m)(m + 2)

Reorder the terms:
0 = (-1 + 4m)(2 + m)

Multiply (-1 + 4m) * (2 + m)
0 = (-1(2 + m) + 4m * (2 + m))
0 = ((2 * -1 + m * -1) + 4m * (2 + m))
0 = ((-2 + -1m) + 4m * (2 + m))
0 = (-2 + -1m + (2 * 4m + m * 4m))
0 = (-2 + -1m + (8m + 4m2))

Combine like terms: -1m + 8m = 7m
0 = (-2 + 7m + 4m2)

Solving
0 = -2 + 7m + 4m2

Solving for variable 'm'.

Combine like terms: 0 + 2 = 2
2 + -7m + -4m2 = -2 + 7m + 4m2 + 2 + -7m + -4m2

Reorder the terms:
2 + -7m + -4m2 = -2 + 2 + 7m + -7m + 4m2 + -4m2

Combine like terms: -2 + 2 = 0
2 + -7m + -4m2 = 0 + 7m + -7m + 4m2 + -4m2
2 + -7m + -4m2 = 7m + -7m + 4m2 + -4m2

Combine like terms: 7m + -7m = 0
2 + -7m + -4m2 = 0 + 4m2 + -4m2
2 + -7m + -4m2 = 4m2 + -4m2

Combine like terms: 4m2 + -4m2 = 0
2 + -7m + -4m2 = 0

Factor a trinomial.
(1 + -4m)(2 + m) = 0

Subproblem 1
Set the factor '(1 + -4m)' equal to zero and attempt to solve:

Simplifying
1 + -4m = 0

Solving
1 + -4m = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4m = 0 + -1
-4m = 0 + -1

Combine like terms: 0 + -1 = -1
-4m = -1

Divide each side by '-4'.
m = 0.25

Simplifying
m = 0.25
Subproblem 2
Set the factor '(2 + m)' equal to zero and attempt to solve:

Simplifying
2 + m = 0

Solving
2 + m = 0

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

Add '-2' to each side of the equation.
2 + -2 + m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + m = 0 + -2
m = 0 + -2

Combine like terms: 0 + -2 = -2
m = -2

Simplifying
m = -2
Solution
m = {0.25, -2}