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

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


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

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

Reorder the terms:
-10x + 4x2 = 3(-5 + 2x)
-10x + 4x2 = (-5 * 3 + 2x * 3)
-10x + 4x2 = (-15 + 6x)

Solving
-10x + 4x2 = -15 + 6x

Solving for variable 'x'.

Reorder the terms:
15 + -10x + -6x + 4x2 = -15 + 6x + 15 + -6x

Combine like terms: -10x + -6x = -16x
15 + -16x + 4x2 = -15 + 6x + 15 + -6x

Reorder the terms:
15 + -16x + 4x2 = -15 + 15 + 6x + -6x

Combine like terms: -15 + 15 = 0
15 + -16x + 4x2 = 0 + 6x + -6x
15 + -16x + 4x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
15 + -16x + 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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