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

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


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

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

Reorder the terms:
10x + x2 = 5(-5 + 4x)
10x + x2 = (-5 * 5 + 4x * 5)
10x + x2 = (-25 + 20x)

Solving
10x + x2 = -25 + 20x

Solving for variable 'x'.

Reorder the terms:
25 + 10x + -20x + x2 = -25 + 20x + 25 + -20x

Combine like terms: 10x + -20x = -10x
25 + -10x + x2 = -25 + 20x + 25 + -20x

Reorder the terms:
25 + -10x + x2 = -25 + 25 + 20x + -20x

Combine like terms: -25 + 25 = 0
25 + -10x + x2 = 0 + 20x + -20x
25 + -10x + x2 = 20x + -20x

Combine like terms: 20x + -20x = 0
25 + -10x + x2 = 0

Factor a trinomial.
(5 + -1x)(5 + -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 '(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 = {5, 5}

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