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

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


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

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

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

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

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

Solving
-28 + -3x + x2 = 12

Solving for variable 'x'.

Reorder the terms:
-28 + -12 + -3x + x2 = 12 + -12

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

Combine like terms: 12 + -12 = 0
-40 + -3x + x2 = 0

Factor a trinomial.
(-5 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve:

Simplifying
-5 + -1x = 0

Solving
-5 + -1x = 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 + -1x = 0 + 5

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

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

Divide each side by '-1'.
x = -5

Simplifying
x = -5

Subproblem 2
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
Solution
x = {-5, 8}

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