(x-6)(x+3)=10

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Solution for (x-6)(x+3)=10 equation: 


Simplifying
(x + -6)(x + 3) = 10

Reorder the terms:
(-6 + x)(x + 3) = 10

Reorder the terms:
(-6 + x)(3 + x) = 10

Multiply (-6 + x) * (3 + x)
(-6(3 + x) + x(3 + x)) = 10
((3 * -6 + x * -6) + x(3 + x)) = 10
((-18 + -6x) + x(3 + x)) = 10
(-18 + -6x + (3 * x + x * x)) = 10
(-18 + -6x + (3x + x2)) = 10

Combine like terms: -6x + 3x = -3x
(-18 + -3x + x2) = 10

Solving
-18 + -3x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-18 + -10 + -3x + x2 = 10 + -10

Combine like terms: -18 + -10 = -28
-28 + -3x + x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-28 + -3x + x2 = 0

Factor a trinomial.
(-4 + -1x)(7 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 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 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {-4, 7}

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