12(x+1)(x-1)=7x

Solution for 12(x+1)(x-1)=7x equation:

Simplifying
12(x + 1)(x + -1) = 7x

Reorder the terms:
12(1 + x)(x + -1) = 7x

Reorder the terms:
12(1 + x)(-1 + x) = 7x

Multiply (1 + x) * (-1 + x)
12(1(-1 + x) + x(-1 + x)) = 7x
12((-1 * 1 + x * 1) + x(-1 + x)) = 7x
12((-1 + 1x) + x(-1 + x)) = 7x
12(-1 + 1x + (-1 * x + x * x)) = 7x
12(-1 + 1x + (-1x + x2)) = 7x

Combine like terms: 1x + -1x = 0
12(-1 + 0 + x2) = 7x
12(-1 + x2) = 7x
(-1 * 12 + x2 * 12) = 7x
(-12 + 12x2) = 7x

Solving
-12 + 12x2 = 7x

Solving for variable 'x'.

Reorder the terms:
-12 + -7x + 12x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-12 + -7x + 12x2 = 0

Factor a trinomial.
(-3 + -4x)(4 + -3x) = 0

Subproblem 1
Set the factor '(-3 + -4x)' equal to zero and attempt to solve:

Simplifying
-3 + -4x = 0

Solving
-3 + -4x = 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 + -4x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4x = 0 + 3
-4x = 0 + 3

Combine like terms: 0 + 3 = 3
-4x = 3

Divide each side by '-4'.
x = -0.75

Simplifying
x = -0.75
Subproblem 2
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Solution
x = {-0.75, 1.333333333}