5x^2+43=(x-1)(x+2)

Solution for 5x^2+43=(x-1)(x+2) equation:

Simplifying
5x2 + 43 = (x + -1)(x + 2)

Reorder the terms:
43 + 5x2 = (x + -1)(x + 2)

Reorder the terms:
43 + 5x2 = (-1 + x)(x + 2)

Reorder the terms:
43 + 5x2 = (-1 + x)(2 + x)

Multiply (-1 + x) * (2 + x)
43 + 5x2 = (-1(2 + x) + x(2 + x))
43 + 5x2 = ((2 * -1 + x * -1) + x(2 + x))
43 + 5x2 = ((-2 + -1x) + x(2 + x))
43 + 5x2 = (-2 + -1x + (2 * x + x * x))
43 + 5x2 = (-2 + -1x + (2x + x2))

Combine like terms: -1x + 2x = 1x
43 + 5x2 = (-2 + 1x + x2)

Solving
43 + 5x2 = -2 + 1x + x2

Solving for variable 'x'.

Reorder the terms:
43 + 2 + -1x + 5x2 + -1x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Combine like terms: 43 + 2 = 45
45 + -1x + 5x2 + -1x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Combine like terms: 5x2 + -1x2 = 4x2
45 + -1x + 4x2 = -2 + 1x + x2 + 2 + -1x + -1x2

Reorder the terms:
45 + -1x + 4x2 = -2 + 2 + 1x + -1x + x2 + -1x2

Combine like terms: -2 + 2 = 0
45 + -1x + 4x2 = 0 + 1x + -1x + x2 + -1x2
45 + -1x + 4x2 = 1x + -1x + x2 + -1x2

Combine like terms: 1x + -1x = 0
45 + -1x + 4x2 = 0 + x2 + -1x2
45 + -1x + 4x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
45 + -1x + 4x2 = 0

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

Divide each side by '4'.
11.25 + -0.25x + x2 = 0

Move the constant term to the right:

Add '-11.25' to each side of the equation.
11.25 + -0.25x + -11.25 + x2 = 0 + -11.25

Reorder the terms:
11.25 + -11.25 + -0.25x + x2 = 0 + -11.25

Combine like terms: 11.25 + -11.25 = 0.00
0.00 + -0.25x + x2 = 0 + -11.25
-0.25x + x2 = 0 + -11.25

Combine like terms: 0 + -11.25 = -11.25
-0.25x + x2 = -11.25

The x term is -0.25x.  Take half its coefficient (-0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
-0.25x + 0.015625 + x2 = -11.25 + 0.015625

Reorder the terms:
0.015625 + -0.25x + x2 = -11.25 + 0.015625

Combine like terms: -11.25 + 0.015625 = -11.234375
0.015625 + -0.25x + x2 = -11.234375

Factor a perfect square on the left side:
(x + -0.125)(x + -0.125) = -11.234375

Can't calculate square root of the right side.

The solution to this equation could not be determined.