(5m-3)(m+2)=(4m+7)(m+1)

Solution for (5m-3)(m+2)=(4m+7)(m+1) equation:

Simplifying
(5m + -3)(m + 2) = (4m + 7)(m + 1)

Reorder the terms:
(-3 + 5m)(m + 2) = (4m + 7)(m + 1)

Reorder the terms:
(-3 + 5m)(2 + m) = (4m + 7)(m + 1)

Multiply (-3 + 5m) * (2 + m)
(-3(2 + m) + 5m * (2 + m)) = (4m + 7)(m + 1)
((2 * -3 + m * -3) + 5m * (2 + m)) = (4m + 7)(m + 1)
((-6 + -3m) + 5m * (2 + m)) = (4m + 7)(m + 1)
(-6 + -3m + (2 * 5m + m * 5m)) = (4m + 7)(m + 1)
(-6 + -3m + (10m + 5m2)) = (4m + 7)(m + 1)

Combine like terms: -3m + 10m = 7m
(-6 + 7m + 5m2) = (4m + 7)(m + 1)

Reorder the terms:
-6 + 7m + 5m2 = (7 + 4m)(m + 1)

Reorder the terms:
-6 + 7m + 5m2 = (7 + 4m)(1 + m)

Multiply (7 + 4m) * (1 + m)
-6 + 7m + 5m2 = (7(1 + m) + 4m * (1 + m))
-6 + 7m + 5m2 = ((1 * 7 + m * 7) + 4m * (1 + m))
-6 + 7m + 5m2 = ((7 + 7m) + 4m * (1 + m))
-6 + 7m + 5m2 = (7 + 7m + (1 * 4m + m * 4m))
-6 + 7m + 5m2 = (7 + 7m + (4m + 4m2))

Combine like terms: 7m + 4m = 11m
-6 + 7m + 5m2 = (7 + 11m + 4m2)

Solving
-6 + 7m + 5m2 = 7 + 11m + 4m2

Solving for variable 'm'.

Reorder the terms:
-6 + -7 + 7m + -11m + 5m2 + -4m2 = 7 + 11m + 4m2 + -7 + -11m + -4m2

Combine like terms: -6 + -7 = -13
-13 + 7m + -11m + 5m2 + -4m2 = 7 + 11m + 4m2 + -7 + -11m + -4m2

Combine like terms: 7m + -11m = -4m
-13 + -4m + 5m2 + -4m2 = 7 + 11m + 4m2 + -7 + -11m + -4m2

Combine like terms: 5m2 + -4m2 = 1m2
-13 + -4m + 1m2 = 7 + 11m + 4m2 + -7 + -11m + -4m2

Reorder the terms:
-13 + -4m + 1m2 = 7 + -7 + 11m + -11m + 4m2 + -4m2

Combine like terms: 7 + -7 = 0
-13 + -4m + 1m2 = 0 + 11m + -11m + 4m2 + -4m2
-13 + -4m + 1m2 = 11m + -11m + 4m2 + -4m2

Combine like terms: 11m + -11m = 0
-13 + -4m + 1m2 = 0 + 4m2 + -4m2
-13 + -4m + 1m2 = 4m2 + -4m2

Combine like terms: 4m2 + -4m2 = 0
-13 + -4m + 1m2 = 0

Begin completing the square.

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + -4m + 13 + m2 = 0 + 13

Reorder the terms:
-13 + 13 + -4m + m2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -4m + m2 = 0 + 13
-4m + m2 = 0 + 13

Combine like terms: 0 + 13 = 13
-4m + m2 = 13

The m term is -4m.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4m + 4 + m2 = 13 + 4

Reorder the terms:
4 + -4m + m2 = 13 + 4

Combine like terms: 13 + 4 = 17
4 + -4m + m2 = 17

Factor a perfect square on the left side:
(m + -2)(m + -2) = 17

Calculate the square root of the right side: 4.123105626

Break this problem into two subproblems by setting 
(m + -2) equal to 4.123105626 and -4.123105626.

Subproblem 1
m + -2 = 4.123105626

Simplifying
m + -2 = 4.123105626

Reorder the terms:
-2 + m = 4.123105626

Solving
-2 + m = 4.123105626

Solving for variable 'm'.

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 = 4.123105626 + 2

Combine like terms: -2 + 2 = 0
0 + m = 4.123105626 + 2
m = 4.123105626 + 2

Combine like terms: 4.123105626 + 2 = 6.123105626
m = 6.123105626

Simplifying
m = 6.123105626

Subproblem 2
m + -2 = -4.123105626

Simplifying
m + -2 = -4.123105626

Reorder the terms:
-2 + m = -4.123105626

Solving
-2 + m = -4.123105626

Solving for variable 'm'.

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 = -4.123105626 + 2

Combine like terms: -2 + 2 = 0
0 + m = -4.123105626 + 2
m = -4.123105626 + 2

Combine like terms: -4.123105626 + 2 = -2.123105626
m = -2.123105626

Simplifying
m = -2.123105626

Solution
The solution to the problem is based on the solutions
from the subproblems.
m = {6.123105626, -2.123105626}