5x^2-(x+2)(x-3)=0

Solution for 5x^2-(x+2)(x-3)=0 equation:

Simplifying
5x2 + -1(x + 2)(x + -3) = 0

Reorder the terms:
5x2 + -1(2 + x)(x + -3) = 0

Reorder the terms:
5x2 + -1(2 + x)(-3 + x) = 0

Multiply (2 + x) * (-3 + x)
5x2 + -1(2(-3 + x) + x(-3 + x)) = 0
5x2 + -1((-3 * 2 + x * 2) + x(-3 + x)) = 0
5x2 + -1((-6 + 2x) + x(-3 + x)) = 0
5x2 + -1(-6 + 2x + (-3 * x + x * x)) = 0
5x2 + -1(-6 + 2x + (-3x + x2)) = 0

Combine like terms: 2x + -3x = -1x
5x2 + -1(-6 + -1x + x2) = 0
5x2 + (-6 * -1 + -1x * -1 + x2 * -1) = 0
5x2 + (6 + 1x + -1x2) = 0

Reorder the terms:
6 + 1x + 5x2 + -1x2 = 0

Combine like terms: 5x2 + -1x2 = 4x2
6 + 1x + 4x2 = 0

Solving
6 + 1x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
1.5 + 0.25x + x2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.25x + -1.5 + x2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.25x + x2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.25x + x2 = 0 + -1.5
0.25x + x2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.25x + x2 = -1.5

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 = -1.5 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = -1.5 + 0.015625

Combine like terms: -1.5 + 0.015625 = -1.484375
0.015625 + 0.25x + x2 = -1.484375

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = -1.484375

Can't calculate square root of the right side.

The solution to this equation could not be determined.