4x(x-5)-5x(x-4)=-1

Solution for 4x(x-5)-5x(x-4)=-1 equation:

Simplifying
4x(x + -5) + -5x(x + -4) = -1

Reorder the terms:
4x(-5 + x) + -5x(x + -4) = -1
(-5 * 4x + x * 4x) + -5x(x + -4) = -1
(-20x + 4x2) + -5x(x + -4) = -1

Reorder the terms:
-20x + 4x2 + -5x(-4 + x) = -1
-20x + 4x2 + (-4 * -5x + x * -5x) = -1
-20x + 4x2 + (20x + -5x2) = -1

Reorder the terms:
-20x + 20x + 4x2 + -5x2 = -1

Combine like terms: -20x + 20x = 0
0 + 4x2 + -5x2 = -1
4x2 + -5x2 = -1

Combine like terms: 4x2 + -5x2 = -1x2
-1x2 = -1

Solving
-1x2 = -1

Solving for variable 'x'.

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

Divide each side by '-1'.
x2 = 1

Simplifying
x2 = 1

Take the square root of each side:
x = {-1, 1}