(5x-6)(x+1)=0

Solution for (5x-6)(x+1)=0 equation:

Simplifying
(5x + -6)(x + 1) = 0

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

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

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

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

Solving
-6 + -1x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1 + -1x)(6 + -5x) = 0

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

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 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 + -1x = 0 + 1

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

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

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

Simplifying
x = -1
Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve:

Simplifying
6 + -5x = 0

Solving
6 + -5x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -5x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -5x = 0 + -6
-5x = 0 + -6

Combine like terms: 0 + -6 = -6
-5x = -6

Divide each side by '-5'.
x = 1.2

Simplifying
x = 1.2
Solution
x = {-1, 1.2}