3(2x-1)(x-3)=4x^2-1

Solution for 3(2x-1)(x-3)=4x^2-1 equation:

Simplifying
3(2x + -1)(x + -3) = 4x2 + -1

Reorder the terms:
3(-1 + 2x)(x + -3) = 4x2 + -1

Reorder the terms:
3(-1 + 2x)(-3 + x) = 4x2 + -1

Multiply (-1 + 2x) * (-3 + x)
3(-1(-3 + x) + 2x * (-3 + x)) = 4x2 + -1
3((-3 * -1 + x * -1) + 2x * (-3 + x)) = 4x2 + -1
3((3 + -1x) + 2x * (-3 + x)) = 4x2 + -1
3(3 + -1x + (-3 * 2x + x * 2x)) = 4x2 + -1
3(3 + -1x + (-6x + 2x2)) = 4x2 + -1

Combine like terms: -1x + -6x = -7x
3(3 + -7x + 2x2) = 4x2 + -1
(3 * 3 + -7x * 3 + 2x2 * 3) = 4x2 + -1
(9 + -21x + 6x2) = 4x2 + -1

Reorder the terms:
9 + -21x + 6x2 = -1 + 4x2

Solving
9 + -21x + 6x2 = -1 + 4x2

Solving for variable 'x'.

Reorder the terms:
9 + 1 + -21x + 6x2 + -4x2 = -1 + 4x2 + 1 + -4x2

Combine like terms: 9 + 1 = 10
10 + -21x + 6x2 + -4x2 = -1 + 4x2 + 1 + -4x2

Combine like terms: 6x2 + -4x2 = 2x2
10 + -21x + 2x2 = -1 + 4x2 + 1 + -4x2

Reorder the terms:
10 + -21x + 2x2 = -1 + 1 + 4x2 + -4x2

Combine like terms: -1 + 1 = 0
10 + -21x + 2x2 = 0 + 4x2 + -4x2
10 + -21x + 2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
10 + -21x + 2x2 = 0

Factor a trinomial.
(1 + -2x)(10 + -1x) = 0

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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2x = 0 + -1
-2x = 0 + -1

Combine like terms: 0 + -1 = -1
-2x = -1

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5
Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve:

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1x = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1x = 0 + -10
-1x = 0 + -10

Combine like terms: 0 + -10 = -10
-1x = -10

Divide each side by '-1'.
x = 10

Simplifying
x = 10
Solution
x = {0.5, 10}