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

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


Simplifying
5x + (2 + -1x)(2 + -1x) = 10

Multiply (2 + -1x) * (2 + -1x)
5x + (2(2 + -1x) + -1x * (2 + -1x)) = 10
5x + ((2 * 2 + -1x * 2) + -1x * (2 + -1x)) = 10
5x + ((4 + -2x) + -1x * (2 + -1x)) = 10
5x + (4 + -2x + (2 * -1x + -1x * -1x)) = 10
5x + (4 + -2x + (-2x + 1x2)) = 10

Combine like terms: -2x + -2x = -4x
5x + (4 + -4x + 1x2) = 10

Reorder the terms:
4 + 5x + -4x + 1x2 = 10

Combine like terms: 5x + -4x = 1x
4 + 1x + 1x2 = 10

Solving
4 + 1x + 1x2 = 10

Solving for variable 'x'.

Reorder the terms:
4 + -10 + 1x + 1x2 = 10 + -10

Combine like terms: 4 + -10 = -6
-6 + 1x + 1x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-6 + 1x + 1x2 = 0

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


Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve:

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1x = 0 + 3
-1x = 0 + 3

Combine like terms: 0 + 3 = 3
-1x = 3

Divide each side by '-1'.
x = -3

Simplifying
x = -3

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 = {-3, 2}

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