x(2x-3)=x^2+10

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Solution for x(2x-3)=x^2+10 equation: 


Simplifying
x(2x + -3) = x2 + 10

Reorder the terms:
x(-3 + 2x) = x2 + 10
(-3 * x + 2x * x) = x2 + 10
(-3x + 2x2) = x2 + 10

Reorder the terms:
-3x + 2x2 = 10 + x2

Solving
-3x + 2x2 = 10 + x2

Solving for variable 'x'.

Reorder the terms:
-10 + -3x + 2x2 + -1x2 = 10 + x2 + -10 + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
-10 + -3x + 1x2 = 10 + x2 + -10 + -1x2

Reorder the terms:
-10 + -3x + 1x2 = 10 + -10 + x2 + -1x2

Combine like terms: 10 + -10 = 0
-10 + -3x + 1x2 = 0 + x2 + -1x2
-10 + -3x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -3x + 1x2 = 0

Factor a trinomial.
(-2 + -1x)(5 + -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 '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-2, 5}

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