4x(x-6)-5x(x-5)=-2

Solution for 4x(x-6)-5x(x-5)=-2 equation:

Simplifying
4x(x + -6) + -5x(x + -5) = -2

Reorder the terms:
4x(-6 + x) + -5x(x + -5) = -2
(-6 * 4x + x * 4x) + -5x(x + -5) = -2
(-24x + 4x2) + -5x(x + -5) = -2

Reorder the terms:
-24x + 4x2 + -5x(-5 + x) = -2
-24x + 4x2 + (-5 * -5x + x * -5x) = -2
-24x + 4x2 + (25x + -5x2) = -2

Reorder the terms:
-24x + 25x + 4x2 + -5x2 = -2

Combine like terms: -24x + 25x = 1x
1x + 4x2 + -5x2 = -2

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

Solving
1x + -1x2 = -2

Solving for variable 'x'.

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

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

Factor a trinomial.
(2 + -1x)(1 + x) = 0

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

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

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

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

Simplifying
x = -1
Solution
x = {2, -1}