2x(2x-5)=3(x-3)

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Solution for 2x(2x-5)=3(x-3) equation: 


Simplifying
2x(2x + -5) = 3(x + -3)

Reorder the terms:
2x(-5 + 2x) = 3(x + -3)
(-5 * 2x + 2x * 2x) = 3(x + -3)
(-10x + 4x2) = 3(x + -3)

Reorder the terms:
-10x + 4x2 = 3(-3 + x)
-10x + 4x2 = (-3 * 3 + x * 3)
-10x + 4x2 = (-9 + 3x)

Solving
-10x + 4x2 = -9 + 3x

Solving for variable 'x'.

Reorder the terms:
9 + -10x + -3x + 4x2 = -9 + 3x + 9 + -3x

Combine like terms: -10x + -3x = -13x
9 + -13x + 4x2 = -9 + 3x + 9 + -3x

Reorder the terms:
9 + -13x + 4x2 = -9 + 9 + 3x + -3x

Combine like terms: -9 + 9 = 0
9 + -13x + 4x2 = 0 + 3x + -3x
9 + -13x + 4x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
9 + -13x + 4x2 = 0

Factor a trinomial.
(1 + -1x)(9 + -4x) = 0


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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1

Subproblem 2
Set the factor '(9 + -4x)' equal to zero and attempt to solve:

Simplifying
9 + -4x = 0

Solving
9 + -4x = 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 + -4x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -4x = 0 + -9
-4x = 0 + -9

Combine like terms: 0 + -9 = -9
-4x = -9

Divide each side by '-4'.
x = 2.25

Simplifying
x = 2.25
Solution
x = {1, 2.25}

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