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

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


Simplifying
3x(2x + -5) + -1x = 5(x + -3)

Reorder the terms:
3x(-5 + 2x) + -1x = 5(x + -3)
(-5 * 3x + 2x * 3x) + -1x = 5(x + -3)
(-15x + 6x2) + -1x = 5(x + -3)

Reorder the terms:
-15x + -1x + 6x2 = 5(x + -3)

Combine like terms: -15x + -1x = -16x
-16x + 6x2 = 5(x + -3)

Reorder the terms:
-16x + 6x2 = 5(-3 + x)
-16x + 6x2 = (-3 * 5 + x * 5)
-16x + 6x2 = (-15 + 5x)

Solving
-16x + 6x2 = -15 + 5x

Solving for variable 'x'.

Reorder the terms:
15 + -16x + -5x + 6x2 = -15 + 5x + 15 + -5x

Combine like terms: -16x + -5x = -21x
15 + -21x + 6x2 = -15 + 5x + 15 + -5x

Reorder the terms:
15 + -21x + 6x2 = -15 + 15 + 5x + -5x

Combine like terms: -15 + 15 = 0
15 + -21x + 6x2 = 0 + 5x + -5x
15 + -21x + 6x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
15 + -21x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(5 + -7x + 2x2) = 0

Factor a trinomial.
3((1 + -1x)(5 + -2x)) = 0

Ignore the factor 3.

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 '(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, 2.5}

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