(4x^2+5x+3)-(9x+7)=

Solution for (4x^2+5x+3)-(9x+7)= equation:

Simplifying
(4x2 + 5x + 3) + -1(9x + 7) = 0

Reorder the terms:
(3 + 5x + 4x2) + -1(9x + 7) = 0

Remove parenthesis around (3 + 5x + 4x2)
3 + 5x + 4x2 + -1(9x + 7) = 0

Reorder the terms:
3 + 5x + 4x2 + -1(7 + 9x) = 0
3 + 5x + 4x2 + (7 * -1 + 9x * -1) = 0
3 + 5x + 4x2 + (-7 + -9x) = 0

Reorder the terms:
3 + -7 + 5x + -9x + 4x2 = 0

Combine like terms: 3 + -7 = -4
-4 + 5x + -9x + 4x2 = 0

Combine like terms: 5x + -9x = -4x
-4 + -4x + 4x2 = 0

Solving
-4 + -4x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-1 + -1x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-1 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + -1x + x2 = 0

Solving
-1 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1 + 0.25

Combine like terms: 1 + 0.25 = 1.25
0.25 + -1x + x2 = 1.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.118033989 and -1.118033989.

Subproblem 1
x + -0.5 = 1.118033989

Simplifying
x + -0.5 = 1.118033989

Reorder the terms:
-0.5 + x = 1.118033989

Solving
-0.5 + x = 1.118033989

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.118033989 + 0.5
x = 1.118033989 + 0.5

Combine like terms: 1.118033989 + 0.5 = 1.618033989
x = 1.618033989

Simplifying
x = 1.618033989

Subproblem 2
x + -0.5 = -1.118033989

Simplifying
x + -0.5 = -1.118033989

Reorder the terms:
-0.5 + x = -1.118033989

Solving
-0.5 + x = -1.118033989

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -1.118033989 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.118033989 + 0.5
x = -1.118033989 + 0.5

Combine like terms: -1.118033989 + 0.5 = -0.618033989
x = -0.618033989

Simplifying
x = -0.618033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.618033989, -0.618033989}
Solution
x = {1.618033989, -0.618033989}