(x-10)(x+7)=0

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Solution for (x-10)(x+7)=0 equation:


Simplifying
(x + -10)(x + 7) = 0

Reorder the terms:
(-10 + x)(x + 7) = 0

Reorder the terms:
(-10 + x)(7 + x) = 0

Multiply (-10 + x) * (7 + x)
(-10(7 + x) + x(7 + x)) = 0
((7 * -10 + x * -10) + x(7 + x)) = 0
((-70 + -10x) + x(7 + x)) = 0
(-70 + -10x + (7 * x + x * x)) = 0
(-70 + -10x + (7x + x2)) = 0

Combine like terms: -10x + 7x = -3x
(-70 + -3x + x2) = 0

Solving
-70 + -3x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-7 + -1x)(10 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {-7, 10}

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