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

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


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

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

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

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

Combine like terms: -4x + 6x = 2x
7x = (-24 + 2x + x2)

Solving
7x = -24 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
24 + 7x + -2x + -1x2 = -24 + 2x + x2 + 24 + -2x + -1x2

Combine like terms: 7x + -2x = 5x
24 + 5x + -1x2 = -24 + 2x + x2 + 24 + -2x + -1x2

Reorder the terms:
24 + 5x + -1x2 = -24 + 24 + 2x + -2x + x2 + -1x2

Combine like terms: -24 + 24 = 0
24 + 5x + -1x2 = 0 + 2x + -2x + x2 + -1x2
24 + 5x + -1x2 = 2x + -2x + x2 + -1x2

Combine like terms: 2x + -2x = 0
24 + 5x + -1x2 = 0 + x2 + -1x2
24 + 5x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
24 + 5x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(3 + x) = 0


Subproblem 1
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8

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

Simplifying
3 + x = 0

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

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

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

Simplifying
x = -3
Solution
x = {8, -3}

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