(x-1)(5x+4)=2

Solution for (x-1)(5x+4)=2 equation:

Simplifying
(x + -1)(5x + 4) = 2

Reorder the terms:
(-1 + x)(5x + 4) = 2

Reorder the terms:
(-1 + x)(4 + 5x) = 2

Multiply (-1 + x) * (4 + 5x)
(-1(4 + 5x) + x(4 + 5x)) = 2
((4 * -1 + 5x * -1) + x(4 + 5x)) = 2
((-4 + -5x) + x(4 + 5x)) = 2
(-4 + -5x + (4 * x + 5x * x)) = 2
(-4 + -5x + (4x + 5x2)) = 2

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

Solving
-4 + -1x + 5x2 = 2

Solving for variable 'x'.

Reorder the terms:
-4 + -2 + -1x + 5x2 = 2 + -2

Combine like terms: -4 + -2 = -6
-6 + -1x + 5x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-6 + -1x + 5x2 = 0

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}