2x(2x-3)=15-2x

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Solution for 2x(2x-3)=15-2x equation: 


Simplifying
2x(2x + -3) = 15 + -2x

Reorder the terms:
2x(-3 + 2x) = 15 + -2x
(-3 * 2x + 2x * 2x) = 15 + -2x
(-6x + 4x2) = 15 + -2x

Solving
-6x + 4x2 = 15 + -2x

Solving for variable 'x'.

Reorder the terms:
-15 + -6x + 2x + 4x2 = 15 + -2x + -15 + 2x

Combine like terms: -6x + 2x = -4x
-15 + -4x + 4x2 = 15 + -2x + -15 + 2x

Reorder the terms:
-15 + -4x + 4x2 = 15 + -15 + -2x + 2x

Combine like terms: 15 + -15 = 0
-15 + -4x + 4x2 = 0 + -2x + 2x
-15 + -4x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-15 + -4x + 4x2 = 0

Factor a trinomial.
(-3 + -2x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-3 + -2x)' equal to zero and attempt to solve:

Simplifying
-3 + -2x = 0

Solving
-3 + -2x = 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 + -2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2x = 0 + 3
-2x = 0 + 3

Combine like terms: 0 + 3 = 3
-2x = 3

Divide each side by '-2'.
x = -1.5

Simplifying
x = -1.5

Subproblem 2
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
Solution
x = {-1.5, 2.5}

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