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

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


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

Reorder the terms:
2x(-2 + x) = 3(x + 10)
(-2 * 2x + x * 2x) = 3(x + 10)
(-4x + 2x2) = 3(x + 10)

Reorder the terms:
-4x + 2x2 = 3(10 + x)
-4x + 2x2 = (10 * 3 + x * 3)
-4x + 2x2 = (30 + 3x)

Solving
-4x + 2x2 = 30 + 3x

Solving for variable 'x'.

Reorder the terms:
-30 + -4x + -3x + 2x2 = 30 + 3x + -30 + -3x

Combine like terms: -4x + -3x = -7x
-30 + -7x + 2x2 = 30 + 3x + -30 + -3x

Reorder the terms:
-30 + -7x + 2x2 = 30 + -30 + 3x + -3x

Combine like terms: 30 + -30 = 0
-30 + -7x + 2x2 = 0 + 3x + -3x
-30 + -7x + 2x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
-30 + -7x + 2x2 = 0

Factor a trinomial.
(-5 + -2x)(6 + -1x) = 0


Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve:

Simplifying
-5 + -2x = 0

Solving
-5 + -2x = 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 + -2x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2x = 0 + 5
-2x = 0 + 5

Combine like terms: 0 + 5 = 5
-2x = 5

Divide each side by '-2'.
x = -2.5

Simplifying
x = -2.5

Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-2.5, 6}

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