x(4x-3)=8x-6

Solution for x(4x-3)=8x-6 equation:

Simplifying
x(4x + -3) = 8x + -6

Reorder the terms:
x(-3 + 4x) = 8x + -6
(-3 * x + 4x * x) = 8x + -6
(-3x + 4x2) = 8x + -6

Reorder the terms:
-3x + 4x2 = -6 + 8x

Solving
-3x + 4x2 = -6 + 8x

Solving for variable 'x'.

Reorder the terms:
6 + -3x + -8x + 4x2 = -6 + 8x + 6 + -8x

Combine like terms: -3x + -8x = -11x
6 + -11x + 4x2 = -6 + 8x + 6 + -8x

Reorder the terms:
6 + -11x + 4x2 = -6 + 6 + 8x + -8x

Combine like terms: -6 + 6 = 0
6 + -11x + 4x2 = 0 + 8x + -8x
6 + -11x + 4x2 = 8x + -8x

Combine like terms: 8x + -8x = 0
6 + -11x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(2 + -1x) = 0

Subproblem 1
Set the factor '(3 + -4x)' equal to zero and attempt to solve:

Simplifying
3 + -4x = 0

Solving
3 + -4x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -4x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4x = 0 + -3
-4x = 0 + -3

Combine like terms: 0 + -3 = -3
-4x = -3

Divide each side by '-4'.
x = 0.75

Simplifying
x = 0.75
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 = {0.75, 2}