x(x-3)+x(x-4)=20-x

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Solution for x(x-3)+x(x-4)=20-x equation:


Simplifying
x(x + -3) + x(x + -4) = 20 + -1x

Reorder the terms:
x(-3 + x) + x(x + -4) = 20 + -1x
(-3 * x + x * x) + x(x + -4) = 20 + -1x
(-3x + x2) + x(x + -4) = 20 + -1x

Reorder the terms:
-3x + x2 + x(-4 + x) = 20 + -1x
-3x + x2 + (-4 * x + x * x) = 20 + -1x
-3x + x2 + (-4x + x2) = 20 + -1x

Reorder the terms:
-3x + -4x + x2 + x2 = 20 + -1x

Combine like terms: -3x + -4x = -7x
-7x + x2 + x2 = 20 + -1x

Combine like terms: x2 + x2 = 2x2
-7x + 2x2 = 20 + -1x

Solving
-7x + 2x2 = 20 + -1x

Solving for variable 'x'.

Reorder the terms:
-20 + -7x + x + 2x2 = 20 + -1x + -20 + x

Combine like terms: -7x + x = -6x
-20 + -6x + 2x2 = 20 + -1x + -20 + x

Reorder the terms:
-20 + -6x + 2x2 = 20 + -20 + -1x + x

Combine like terms: 20 + -20 = 0
-20 + -6x + 2x2 = 0 + -1x + x
-20 + -6x + 2x2 = -1x + x

Combine like terms: -1x + x = 0
-20 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -3x + x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {-2, 5}

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