(x-7)(x+2)=10

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Solution for (x-7)(x+2)=10 equation: 


Simplifying
(x + -7)(x + 2) = 10

Reorder the terms:
(-7 + x)(x + 2) = 10

Reorder the terms:
(-7 + x)(2 + x) = 10

Multiply (-7 + x) * (2 + x)
(-7(2 + x) + x(2 + x)) = 10
((2 * -7 + x * -7) + x(2 + x)) = 10
((-14 + -7x) + x(2 + x)) = 10
(-14 + -7x + (2 * x + x * x)) = 10
(-14 + -7x + (2x + x2)) = 10

Combine like terms: -7x + 2x = -5x
(-14 + -5x + x2) = 10

Solving
-14 + -5x + x2 = 10

Solving for variable 'x'.

Reorder the terms:
-14 + -10 + -5x + x2 = 10 + -10

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

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

Factor a trinomial.
(-3 + -1x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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 = {-3, 8}

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