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

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

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

Reorder the terms:
(1 + x)(x + 4) = 10x

Reorder the terms:
(1 + x)(4 + x) = 10x

Multiply (1 + x) * (4 + x)
(1(4 + x) + x(4 + x)) = 10x
((4 * 1 + x * 1) + x(4 + x)) = 10x
((4 + 1x) + x(4 + x)) = 10x
(4 + 1x + (4 * x + x * x)) = 10x
(4 + 1x + (4x + x2)) = 10x

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

Solving
4 + 5x + x2 = 10x

Solving for variable 'x'.

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

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

Combine like terms: 10x + -10x = 0
4 + -5x + x2 = 0

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

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1
Subproblem 2
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
Solution
x = {1, 4}