(4x+3)(2x-5)+10=(3x^2-1)+x^2

Solution for (4x+3)(2x-5)+10=(3x^2-1)+x^2 equation:

Simplifying
(4x + 3)(2x + -5) + 10 = (3x2 + -1) + x2

Reorder the terms:
(3 + 4x)(2x + -5) + 10 = (3x2 + -1) + x2

Reorder the terms:
(3 + 4x)(-5 + 2x) + 10 = (3x2 + -1) + x2

Multiply (3 + 4x) * (-5 + 2x)
(3(-5 + 2x) + 4x * (-5 + 2x)) + 10 = (3x2 + -1) + x2
((-5 * 3 + 2x * 3) + 4x * (-5 + 2x)) + 10 = (3x2 + -1) + x2
((-15 + 6x) + 4x * (-5 + 2x)) + 10 = (3x2 + -1) + x2
(-15 + 6x + (-5 * 4x + 2x * 4x)) + 10 = (3x2 + -1) + x2
(-15 + 6x + (-20x + 8x2)) + 10 = (3x2 + -1) + x2

Combine like terms: 6x + -20x = -14x
(-15 + -14x + 8x2) + 10 = (3x2 + -1) + x2

Reorder the terms:
-15 + 10 + -14x + 8x2 = (3x2 + -1) + x2

Combine like terms: -15 + 10 = -5
-5 + -14x + 8x2 = (3x2 + -1) + x2

Reorder the terms:
-5 + -14x + 8x2 = (-1 + 3x2) + x2

Remove parenthesis around (-1 + 3x2)
-5 + -14x + 8x2 = -1 + 3x2 + x2

Combine like terms: 3x2 + x2 = 4x2
-5 + -14x + 8x2 = -1 + 4x2

Solving
-5 + -14x + 8x2 = -1 + 4x2

Solving for variable 'x'.

Reorder the terms:
-5 + 1 + -14x + 8x2 + -4x2 = -1 + 4x2 + 1 + -4x2

Combine like terms: -5 + 1 = -4
-4 + -14x + 8x2 + -4x2 = -1 + 4x2 + 1 + -4x2

Combine like terms: 8x2 + -4x2 = 4x2
-4 + -14x + 4x2 = -1 + 4x2 + 1 + -4x2

Reorder the terms:
-4 + -14x + 4x2 = -1 + 1 + 4x2 + -4x2

Combine like terms: -1 + 1 = 0
-4 + -14x + 4x2 = 0 + 4x2 + -4x2
-4 + -14x + 4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-4 + -14x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -7x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -7x + 2x2)' equal to zero and attempt to solve:

Simplifying
-2 + -7x + 2x2 = 0

Solving
-2 + -7x + 2x2 = 0

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

Divide each side by '2'.
-1 + -3.5x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -3.5x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -3.5x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3.5x + x2 = 0 + 1
-3.5x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-3.5x + x2 = 1

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 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 1 + 3.0625

Combine like terms: 1 + 3.0625 = 4.0625
3.0625 + -3.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + -1.75) equal to 2.015564437 and -2.015564437.

Subproblem 1
x + -1.75 = 2.015564437

Simplifying
x + -1.75 = 2.015564437

Reorder the terms:
-1.75 + x = 2.015564437

Solving
-1.75 + x = 2.015564437

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 = 2.015564437 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = 2.015564437 + 1.75
x = 2.015564437 + 1.75

Combine like terms: 2.015564437 + 1.75 = 3.765564437
x = 3.765564437

Simplifying
x = 3.765564437

Subproblem 2
x + -1.75 = -2.015564437

Simplifying
x + -1.75 = -2.015564437

Reorder the terms:
-1.75 + x = -2.015564437

Solving
-1.75 + x = -2.015564437

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 = -2.015564437 + 1.75

Combine like terms: -1.75 + 1.75 = 0.00
0.00 + x = -2.015564437 + 1.75
x = -2.015564437 + 1.75

Combine like terms: -2.015564437 + 1.75 = -0.265564437
x = -0.265564437

Simplifying
x = -0.265564437

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.765564437, -0.265564437}
Solution
x = {3.765564437, -0.265564437}