x(x+10)=5x(x-1)-4

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Solution for x(x+10)=5x(x-1)-4 equation: 


Simplifying
x(x + 10) = 5x(x + -1) + -4

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

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

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

Solving
10x + x2 = -4 + -5x + 5x2

Solving for variable 'x'.

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

Combine like terms: 10x + 5x = 15x
4 + 15x + x2 + -5x2 = -4 + -5x + 5x2 + 4 + 5x + -5x2

Combine like terms: x2 + -5x2 = -4x2
4 + 15x + -4x2 = -4 + -5x + 5x2 + 4 + 5x + -5x2

Reorder the terms:
4 + 15x + -4x2 = -4 + 4 + -5x + 5x + 5x2 + -5x2

Combine like terms: -4 + 4 = 0
4 + 15x + -4x2 = 0 + -5x + 5x + 5x2 + -5x2
4 + 15x + -4x2 = -5x + 5x + 5x2 + -5x2

Combine like terms: -5x + 5x = 0
4 + 15x + -4x2 = 0 + 5x2 + -5x2
4 + 15x + -4x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
4 + 15x + -4x2 = 0

Factor a trinomial.
(4 + -1x)(1 + 4x) = 0


Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {4, -0.25}

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