2x^2+7x+3=12.5(x+3)(x+0.5)

Solution for 2x^2+7x+3=12.5(x+3)(x+0.5) equation:

Simplifying
2x2 + 7x + 3 = 12.5(x + 3)(x + 0.5)

Reorder the terms:
3 + 7x + 2x2 = 12.5(x + 3)(x + 0.5)

Reorder the terms:
3 + 7x + 2x2 = 12.5(3 + x)(x + 0.5)

Reorder the terms:
3 + 7x + 2x2 = 12.5(3 + x)(0.5 + x)

Multiply (3 + x) * (0.5 + x)
3 + 7x + 2x2 = 12.5(3(0.5 + x) + x(0.5 + x))
3 + 7x + 2x2 = 12.5((0.5 * 3 + x * 3) + x(0.5 + x))
3 + 7x + 2x2 = 12.5((1.5 + 3x) + x(0.5 + x))
3 + 7x + 2x2 = 12.5(1.5 + 3x + (0.5 * x + x * x))
3 + 7x + 2x2 = 12.5(1.5 + 3x + (0.5x + x2))

Combine like terms: 3x + 0.5x = 3.5x
3 + 7x + 2x2 = 12.5(1.5 + 3.5x + x2)
3 + 7x + 2x2 = (1.5 * 12.5 + 3.5x * 12.5 + x2 * 12.5)
3 + 7x + 2x2 = (18.75 + 43.75x + 12.5x2)

Solving
3 + 7x + 2x2 = 18.75 + 43.75x + 12.5x2

Solving for variable 'x'.

Reorder the terms:
3 + -18.75 + 7x + -43.75x + 2x2 + -12.5x2 = 18.75 + 43.75x + 12.5x2 + -18.75 + -43.75x + -12.5x2

Combine like terms: 3 + -18.75 = -15.75
-15.75 + 7x + -43.75x + 2x2 + -12.5x2 = 18.75 + 43.75x + 12.5x2 + -18.75 + -43.75x + -12.5x2

Combine like terms: 7x + -43.75x = -36.75x
-15.75 + -36.75x + 2x2 + -12.5x2 = 18.75 + 43.75x + 12.5x2 + -18.75 + -43.75x + -12.5x2

Combine like terms: 2x2 + -12.5x2 = -10.5x2
-15.75 + -36.75x + -10.5x2 = 18.75 + 43.75x + 12.5x2 + -18.75 + -43.75x + -12.5x2

Reorder the terms:
-15.75 + -36.75x + -10.5x2 = 18.75 + -18.75 + 43.75x + -43.75x + 12.5x2 + -12.5x2

Combine like terms: 18.75 + -18.75 = 0.00
-15.75 + -36.75x + -10.5x2 = 0.00 + 43.75x + -43.75x + 12.5x2 + -12.5x2
-15.75 + -36.75x + -10.5x2 = 43.75x + -43.75x + 12.5x2 + -12.5x2

Combine like terms: 43.75x + -43.75x = 0.00
-15.75 + -36.75x + -10.5x2 = 0.00 + 12.5x2 + -12.5x2
-15.75 + -36.75x + -10.5x2 = 12.5x2 + -12.5x2

Combine like terms: 12.5x2 + -12.5x2 = 0.0
-15.75 + -36.75x + -10.5x2 = 0.0

Begin completing the square.  Divide all terms by
-10.5 the coefficient of the squared term: 

Divide each side by '-10.5'.
1.5 + 3.5x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 3.5x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 3.5x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 3.5x + x2 = 0 + -1.5
3.5x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
3.5x + x2 = -1.5

The x term is 3.5x.  Take half its coefficient (1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
3.5x + 3.0625 + x2 = -1.5 + 3.0625

Reorder the terms:
3.0625 + 3.5x + x2 = -1.5 + 3.0625

Combine like terms: -1.5 + 3.0625 = 1.5625
3.0625 + 3.5x + x2 = 1.5625

Factor a perfect square on the left side:
(x + 1.75)(x + 1.75) = 1.5625

Calculate the square root of the right side: 1.25

Break this problem into two subproblems by setting 
(x + 1.75) equal to 1.25 and -1.25.

Subproblem 1
x + 1.75 = 1.25

Simplifying
x + 1.75 = 1.25

Reorder the terms:
1.75 + x = 1.25

Solving
1.75 + x = 1.25

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = 1.25 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = 1.25 + -1.75
x = 1.25 + -1.75

Combine like terms: 1.25 + -1.75 = -0.5
x = -0.5

Simplifying
x = -0.5

Subproblem 2
x + 1.75 = -1.25

Simplifying
x + 1.75 = -1.25

Reorder the terms:
1.75 + x = -1.25

Solving
1.75 + x = -1.25

Solving for variable 'x'.

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

Add '-1.75' to each side of the equation.
1.75 + -1.75 + x = -1.25 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + x = -1.25 + -1.75
x = -1.25 + -1.75

Combine like terms: -1.25 + -1.75 = -3
x = -3

Simplifying
x = -3

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.5, -3}