5x(x-2)-4(x-2)=0

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Solution for 5x(x-2)-4(x-2)=0 equation: 


Simplifying
5x(x + -2) + -4(x + -2) = 0

Reorder the terms:
5x(-2 + x) + -4(x + -2) = 0
(-2 * 5x + x * 5x) + -4(x + -2) = 0
(-10x + 5x2) + -4(x + -2) = 0

Reorder the terms:
-10x + 5x2 + -4(-2 + x) = 0
-10x + 5x2 + (-2 * -4 + x * -4) = 0
-10x + 5x2 + (8 + -4x) = 0

Reorder the terms:
8 + -10x + -4x + 5x2 = 0

Combine like terms: -10x + -4x = -14x
8 + -14x + 5x2 = 0

Solving
8 + -14x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4 + -5x)(2 + -1x) = 0


Subproblem 1
Set the factor '(4 + -5x)' equal to zero and attempt to solve:

Simplifying
4 + -5x = 0

Solving
4 + -5x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -5x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5x = 0 + -4
-5x = 0 + -4

Combine like terms: 0 + -4 = -4
-5x = -4

Divide each side by '-5'.
x = 0.8

Simplifying
x = 0.8

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0.8, 2}

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