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

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Solution for 0=(x+4)(x-6) equation: 


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

Reorder the terms:
0 = (4 + x)(x + -6)

Reorder the terms:
0 = (4 + x)(-6 + x)

Multiply (4 + x) * (-6 + x)
0 = (4(-6 + x) + x(-6 + x))
0 = ((-6 * 4 + x * 4) + x(-6 + x))
0 = ((-24 + 4x) + x(-6 + x))
0 = (-24 + 4x + (-6 * x + x * x))
0 = (-24 + 4x + (-6x + x2))

Combine like terms: 4x + -6x = -2x
0 = (-24 + -2x + x2)

Solving
0 = -24 + -2x + x2

Solving for variable 'x'.

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

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

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

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

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

Factor a trinomial.
(6 + -1x)(4 + x) = 0


Subproblem 1
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6

Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

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

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

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

Simplifying
x = -4
Solution
x = {6, -4}

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