(x+3)(x-8)+10=0

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Solution for (x+3)(x-8)+10=0 equation: 


Simplifying
(x + 3)(x + -8) + 10 = 0

Reorder the terms:
(3 + x)(x + -8) + 10 = 0

Reorder the terms:
(3 + x)(-8 + x) + 10 = 0

Multiply (3 + x) * (-8 + x)
(3(-8 + x) + x(-8 + x)) + 10 = 0
((-8 * 3 + x * 3) + x(-8 + x)) + 10 = 0
((-24 + 3x) + x(-8 + x)) + 10 = 0
(-24 + 3x + (-8 * x + x * x)) + 10 = 0
(-24 + 3x + (-8x + x2)) + 10 = 0

Combine like terms: 3x + -8x = -5x
(-24 + -5x + x2) + 10 = 0

Reorder the terms:
-24 + 10 + -5x + x2 = 0

Combine like terms: -24 + 10 = -14
-14 + -5x + x2 = 0

Solving
-14 + -5x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-2 + -1x)(7 + -1x) = 0


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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

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

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

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 7}

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