(5x-2)*(2x-5)=10

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Solution for (5x-2)*(2x-5)=10 equation: 


Simplifying
(5x + -2)(2x + -5) = 10

Reorder the terms:
(-2 + 5x)(2x + -5) = 10

Reorder the terms:
(-2 + 5x)(-5 + 2x) = 10

Multiply (-2 + 5x) * (-5 + 2x)
(-2(-5 + 2x) + 5x * (-5 + 2x)) = 10
((-5 * -2 + 2x * -2) + 5x * (-5 + 2x)) = 10
((10 + -4x) + 5x * (-5 + 2x)) = 10
(10 + -4x + (-5 * 5x + 2x * 5x)) = 10
(10 + -4x + (-25x + 10x2)) = 10

Combine like terms: -4x + -25x = -29x
(10 + -29x + 10x2) = 10

Add '-10' to each side of the equation.
10 + -29x + -10 + 10x2 = 10 + -10

Reorder the terms:
10 + -10 + -29x + 10x2 = 10 + -10

Combine like terms: 10 + -10 = 0
0 + -29x + 10x2 = 10 + -10
-29x + 10x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-29x + 10x2 = 0

Solving
-29x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-29 + 10x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-29 + 10x)' equal to zero and attempt to solve:

Simplifying
-29 + 10x = 0

Solving
-29 + 10x = 0

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

Add '29' to each side of the equation.
-29 + 29 + 10x = 0 + 29

Combine like terms: -29 + 29 = 0
0 + 10x = 0 + 29
10x = 0 + 29

Combine like terms: 0 + 29 = 29
10x = 29

Divide each side by '10'.
x = 2.9

Simplifying
x = 2.9
Solution
x = {0, 2.9}

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