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

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

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

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

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

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

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

Solving
5x = -6 + 6x2

Solving for variable 'x'.

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

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

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

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

Factor a trinomial.
(3 + -2x)(2 + 3x) = 0

Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 2
Set the factor '(2 + 3x)' equal to zero and attempt to solve:

Simplifying
2 + 3x = 0

Solving
2 + 3x = 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 + 3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3x = 0 + -2
3x = 0 + -2

Combine like terms: 0 + -2 = -2
3x = -2

Divide each side by '3'.
x = -0.6666666667

Simplifying
x = -0.6666666667
Solution
x = {1.5, -0.6666666667}