4x(-5+x)=10-2x

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Solution for 4x(-5+x)=10-2x equation: 


Simplifying
4x(-5 + x) = 10 + -2x
(-5 * 4x + x * 4x) = 10 + -2x
(-20x + 4x2) = 10 + -2x

Solving
-20x + 4x2 = 10 + -2x

Solving for variable 'x'.

Reorder the terms:
-10 + -20x + 2x + 4x2 = 10 + -2x + -10 + 2x

Combine like terms: -20x + 2x = -18x
-10 + -18x + 4x2 = 10 + -2x + -10 + 2x

Reorder the terms:
-10 + -18x + 4x2 = 10 + -10 + -2x + 2x

Combine like terms: 10 + -10 = 0
-10 + -18x + 4x2 = 0 + -2x + 2x
-10 + -18x + 4x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-10 + -18x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -9x + 2x2) = 0

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

Ignore the factor 2.

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

Simplifying
-1 + -2x = 0

Solving
-1 + -2x = 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 + -2x = 0 + 1

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

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

Divide each side by '-2'.
x = -0.5

Simplifying
x = -0.5

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-0.5, 5}

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