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

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


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

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

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

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

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

Solving
-18 + 3x + x2 = 10x

Solving for variable 'x'.

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

Combine like terms: 3x + -10x = -7x
-18 + -7x + x2 = 10x + -10x

Combine like terms: 10x + -10x = 0
-18 + -7x + x2 = 0

Factor a trinomial.
(-2 + -1x)(9 + -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 '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-2, 9}

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