(4x+6)(x-1)=25x

Solution for (4x+6)(x-1)=25x equation:

Simplifying
(4x + 6)(x + -1) = 25x

Reorder the terms:
(6 + 4x)(x + -1) = 25x

Reorder the terms:
(6 + 4x)(-1 + x) = 25x

Multiply (6 + 4x) * (-1 + x)
(6(-1 + x) + 4x * (-1 + x)) = 25x
((-1 * 6 + x * 6) + 4x * (-1 + x)) = 25x
((-6 + 6x) + 4x * (-1 + x)) = 25x
(-6 + 6x + (-1 * 4x + x * 4x)) = 25x
(-6 + 6x + (-4x + 4x2)) = 25x

Combine like terms: 6x + -4x = 2x
(-6 + 2x + 4x2) = 25x

Solving
-6 + 2x + 4x2 = 25x

Solving for variable 'x'.

Reorder the terms:
-6 + 2x + -25x + 4x2 = 25x + -25x

Combine like terms: 2x + -25x = -23x
-6 + -23x + 4x2 = 25x + -25x

Combine like terms: 25x + -25x = 0
-6 + -23x + 4x2 = 0

Factor a trinomial.
(-1 + -4x)(6 + -1x) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {-0.25, 6}