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

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Solution for (2x-5)(2-3x+1)= equation: 


Simplifying
(2x + -5)(2 + -3x + 1) = 0

Reorder the terms:
(-5 + 2x)(2 + -3x + 1) = 0

Reorder the terms:
(-5 + 2x)(2 + 1 + -3x) = 0

Combine like terms: 2 + 1 = 3
(-5 + 2x)(3 + -3x) = 0

Multiply (-5 + 2x) * (3 + -3x)
(-5(3 + -3x) + 2x * (3 + -3x)) = 0
((3 * -5 + -3x * -5) + 2x * (3 + -3x)) = 0
((-15 + 15x) + 2x * (3 + -3x)) = 0
(-15 + 15x + (3 * 2x + -3x * 2x)) = 0
(-15 + 15x + (6x + -6x2)) = 0

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

Solving
-15 + 21x + -6x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 3.

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 '(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
Solution
x = {2.5, 1}

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