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

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Solution for 12=(x+4)(x-7) equation: 


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

Reorder the terms:
12 = (4 + x)(x + -7)

Reorder the terms:
12 = (4 + x)(-7 + x)

Multiply (4 + x) * (-7 + x)
12 = (4(-7 + x) + x(-7 + x))
12 = ((-7 * 4 + x * 4) + x(-7 + x))
12 = ((-28 + 4x) + x(-7 + x))
12 = (-28 + 4x + (-7 * x + x * x))
12 = (-28 + 4x + (-7x + x2))

Combine like terms: 4x + -7x = -3x
12 = (-28 + -3x + x2)

Solving
12 = -28 + -3x + x2

Solving for variable 'x'.

Combine like terms: 12 + 28 = 40
40 + 3x + -1x2 = -28 + -3x + x2 + 28 + 3x + -1x2

Reorder the terms:
40 + 3x + -1x2 = -28 + 28 + -3x + 3x + x2 + -1x2

Combine like terms: -28 + 28 = 0
40 + 3x + -1x2 = 0 + -3x + 3x + x2 + -1x2
40 + 3x + -1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
40 + 3x + -1x2 = 0 + x2 + -1x2
40 + 3x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
40 + 3x + -1x2 = 0

Factor a trinomial.
(8 + -1x)(5 + 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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

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

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

Simplifying
x = -5
Solution
x = {8, -5}

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