(7x-6)(x+4)=(1-2x)(x-6)

Solution for (7x-6)(x+4)=(1-2x)(x-6) equation:

Simplifying
(7x + -6)(x + 4) = (1 + -2x)(x + -6)

Reorder the terms:
(-6 + 7x)(x + 4) = (1 + -2x)(x + -6)

Reorder the terms:
(-6 + 7x)(4 + x) = (1 + -2x)(x + -6)

Multiply (-6 + 7x) * (4 + x)
(-6(4 + x) + 7x * (4 + x)) = (1 + -2x)(x + -6)
((4 * -6 + x * -6) + 7x * (4 + x)) = (1 + -2x)(x + -6)
((-24 + -6x) + 7x * (4 + x)) = (1 + -2x)(x + -6)
(-24 + -6x + (4 * 7x + x * 7x)) = (1 + -2x)(x + -6)
(-24 + -6x + (28x + 7x2)) = (1 + -2x)(x + -6)

Combine like terms: -6x + 28x = 22x
(-24 + 22x + 7x2) = (1 + -2x)(x + -6)

Reorder the terms:
-24 + 22x + 7x2 = (1 + -2x)(-6 + x)

Multiply (1 + -2x) * (-6 + x)
-24 + 22x + 7x2 = (1(-6 + x) + -2x * (-6 + x))
-24 + 22x + 7x2 = ((-6 * 1 + x * 1) + -2x * (-6 + x))
-24 + 22x + 7x2 = ((-6 + 1x) + -2x * (-6 + x))
-24 + 22x + 7x2 = (-6 + 1x + (-6 * -2x + x * -2x))
-24 + 22x + 7x2 = (-6 + 1x + (12x + -2x2))

Combine like terms: 1x + 12x = 13x
-24 + 22x + 7x2 = (-6 + 13x + -2x2)

Solving
-24 + 22x + 7x2 = -6 + 13x + -2x2

Solving for variable 'x'.

Reorder the terms:
-24 + 6 + 22x + -13x + 7x2 + 2x2 = -6 + 13x + -2x2 + 6 + -13x + 2x2

Combine like terms: -24 + 6 = -18
-18 + 22x + -13x + 7x2 + 2x2 = -6 + 13x + -2x2 + 6 + -13x + 2x2

Combine like terms: 22x + -13x = 9x
-18 + 9x + 7x2 + 2x2 = -6 + 13x + -2x2 + 6 + -13x + 2x2

Combine like terms: 7x2 + 2x2 = 9x2
-18 + 9x + 9x2 = -6 + 13x + -2x2 + 6 + -13x + 2x2

Reorder the terms:
-18 + 9x + 9x2 = -6 + 6 + 13x + -13x + -2x2 + 2x2

Combine like terms: -6 + 6 = 0
-18 + 9x + 9x2 = 0 + 13x + -13x + -2x2 + 2x2
-18 + 9x + 9x2 = 13x + -13x + -2x2 + 2x2

Combine like terms: 13x + -13x = 0
-18 + 9x + 9x2 = 0 + -2x2 + 2x2
-18 + 9x + 9x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-18 + 9x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '9'.
9(-2 + x + x2) = 0

Factor a trinomial.
9((-2 + -1x)(1 + -1x)) = 0

Ignore the factor 9.
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 + -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
Solution
x = {-2, 1}