(.7d+1)(1.5d-2)=(2.5+d)(4-1.3d)

Solution for (.7d+1)(1.5d-2)=(2.5+d)(4-1.3d) equation:

Simplifying
(0.7d + 1)(1.5d + -2) = (2.5 + d)(4 + -1.3d)

Reorder the terms:
(1 + 0.7d)(1.5d + -2) = (2.5 + d)(4 + -1.3d)

Reorder the terms:
(1 + 0.7d)(-2 + 1.5d) = (2.5 + d)(4 + -1.3d)

Multiply (1 + 0.7d) * (-2 + 1.5d)
(1(-2 + 1.5d) + 0.7d * (-2 + 1.5d)) = (2.5 + d)(4 + -1.3d)
((-2 * 1 + 1.5d * 1) + 0.7d * (-2 + 1.5d)) = (2.5 + d)(4 + -1.3d)
((-2 + 1.5d) + 0.7d * (-2 + 1.5d)) = (2.5 + d)(4 + -1.3d)
(-2 + 1.5d + (-2 * 0.7d + 1.5d * 0.7d)) = (2.5 + d)(4 + -1.3d)
(-2 + 1.5d + (-1.4d + 1.05d2)) = (2.5 + d)(4 + -1.3d)

Combine like terms: 1.5d + -1.4d = 0.1d
(-2 + 0.1d + 1.05d2) = (2.5 + d)(4 + -1.3d)

Multiply (2.5 + d) * (4 + -1.3d)
-2 + 0.1d + 1.05d2 = (2.5(4 + -1.3d) + d(4 + -1.3d))
-2 + 0.1d + 1.05d2 = ((4 * 2.5 + -1.3d * 2.5) + d(4 + -1.3d))
-2 + 0.1d + 1.05d2 = ((10 + -3.25d) + d(4 + -1.3d))
-2 + 0.1d + 1.05d2 = (10 + -3.25d + (4 * d + -1.3d * d))
-2 + 0.1d + 1.05d2 = (10 + -3.25d + (4d + -1.3d2))

Combine like terms: -3.25d + 4d = 0.75d
-2 + 0.1d + 1.05d2 = (10 + 0.75d + -1.3d2)

Solving
-2 + 0.1d + 1.05d2 = 10 + 0.75d + -1.3d2

Solving for variable 'd'.

Reorder the terms:
-2 + -10 + 0.1d + -0.75d + 1.05d2 + 1.3d2 = 10 + 0.75d + -1.3d2 + -10 + -0.75d + 1.3d2

Combine like terms: -2 + -10 = -12
-12 + 0.1d + -0.75d + 1.05d2 + 1.3d2 = 10 + 0.75d + -1.3d2 + -10 + -0.75d + 1.3d2

Combine like terms: 0.1d + -0.75d = -0.65d
-12 + -0.65d + 1.05d2 + 1.3d2 = 10 + 0.75d + -1.3d2 + -10 + -0.75d + 1.3d2

Combine like terms: 1.05d2 + 1.3d2 = 2.35d2
-12 + -0.65d + 2.35d2 = 10 + 0.75d + -1.3d2 + -10 + -0.75d + 1.3d2

Reorder the terms:
-12 + -0.65d + 2.35d2 = 10 + -10 + 0.75d + -0.75d + -1.3d2 + 1.3d2

Combine like terms: 10 + -10 = 0
-12 + -0.65d + 2.35d2 = 0 + 0.75d + -0.75d + -1.3d2 + 1.3d2
-12 + -0.65d + 2.35d2 = 0.75d + -0.75d + -1.3d2 + 1.3d2

Combine like terms: 0.75d + -0.75d = 0.00
-12 + -0.65d + 2.35d2 = 0.00 + -1.3d2 + 1.3d2
-12 + -0.65d + 2.35d2 = -1.3d2 + 1.3d2

Combine like terms: -1.3d2 + 1.3d2 = 0.0
-12 + -0.65d + 2.35d2 = 0.0

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

Divide each side by '2.35'.
-5.106382979 + -0.2765957447d + d2 = 0

Move the constant term to the right:

Add '5.106382979' to each side of the equation.
-5.106382979 + -0.2765957447d + 5.106382979 + d2 = 0 + 5.106382979

Reorder the terms:
-5.106382979 + 5.106382979 + -0.2765957447d + d2 = 0 + 5.106382979

Combine like terms: -5.106382979 + 5.106382979 = 0.000000000
0.000000000 + -0.2765957447d + d2 = 0 + 5.106382979
-0.2765957447d + d2 = 0 + 5.106382979

Combine like terms: 0 + 5.106382979 = 5.106382979
-0.2765957447d + d2 = 5.106382979

The d term is -0.2765957447d.  Take half its coefficient (-0.1382978724).
Square it (0.01912630151) and add it to both sides.

Add '0.01912630151' to each side of the equation.
-0.2765957447d + 0.01912630151 + d2 = 5.106382979 + 0.01912630151

Reorder the terms:
0.01912630151 + -0.2765957447d + d2 = 5.106382979 + 0.01912630151

Combine like terms: 5.106382979 + 0.01912630151 = 5.12550928051
0.01912630151 + -0.2765957447d + d2 = 5.12550928051

Factor a perfect square on the left side:
(d + -0.1382978724)(d + -0.1382978724) = 5.12550928051

Calculate the square root of the right side: 2.263958763

Break this problem into two subproblems by setting 
(d + -0.1382978724) equal to 2.263958763 and -2.263958763.

Subproblem 1
d + -0.1382978724 = 2.263958763

Simplifying
d + -0.1382978724 = 2.263958763

Reorder the terms:
-0.1382978724 + d = 2.263958763

Solving
-0.1382978724 + d = 2.263958763

Solving for variable 'd'.

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

Add '0.1382978724' to each side of the equation.
-0.1382978724 + 0.1382978724 + d = 2.263958763 + 0.1382978724

Combine like terms: -0.1382978724 + 0.1382978724 = 0.0000000000
0.0000000000 + d = 2.263958763 + 0.1382978724
d = 2.263958763 + 0.1382978724

Combine like terms: 2.263958763 + 0.1382978724 = 2.4022566354
d = 2.4022566354

Simplifying
d = 2.4022566354

Subproblem 2
d + -0.1382978724 = -2.263958763

Simplifying
d + -0.1382978724 = -2.263958763

Reorder the terms:
-0.1382978724 + d = -2.263958763

Solving
-0.1382978724 + d = -2.263958763

Solving for variable 'd'.

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

Add '0.1382978724' to each side of the equation.
-0.1382978724 + 0.1382978724 + d = -2.263958763 + 0.1382978724

Combine like terms: -0.1382978724 + 0.1382978724 = 0.0000000000
0.0000000000 + d = -2.263958763 + 0.1382978724
d = -2.263958763 + 0.1382978724

Combine like terms: -2.263958763 + 0.1382978724 = -2.1256608906
d = -2.1256608906

Simplifying
d = -2.1256608906

Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {2.4022566354, -2.1256608906}