x(x-3)+4x=-2(x-5)

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Solution for x(x-3)+4x=-2(x-5) equation: 


Simplifying
x(x + -3) + 4x = -2(x + -5)

Reorder the terms:
x(-3 + x) + 4x = -2(x + -5)
(-3 * x + x * x) + 4x = -2(x + -5)
(-3x + x2) + 4x = -2(x + -5)

Reorder the terms:
-3x + 4x + x2 = -2(x + -5)

Combine like terms: -3x + 4x = 1x
1x + x2 = -2(x + -5)

Reorder the terms:
1x + x2 = -2(-5 + x)
1x + x2 = (-5 * -2 + x * -2)
1x + x2 = (10 + -2x)

Solving
1x + x2 = 10 + -2x

Solving for variable 'x'.

Reorder the terms:
-10 + 1x + 2x + x2 = 10 + -2x + -10 + 2x

Combine like terms: 1x + 2x = 3x
-10 + 3x + x2 = 10 + -2x + -10 + 2x

Reorder the terms:
-10 + 3x + x2 = 10 + -10 + -2x + 2x

Combine like terms: 10 + -10 = 0
-10 + 3x + x2 = 0 + -2x + 2x
-10 + 3x + x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
-10 + 3x + x2 = 0

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


Subproblem 1
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

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 = {-5, 2}

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