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

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


Simplifying
0 = (2x + -3)(4x + -3)

Reorder the terms:
0 = (-3 + 2x)(4x + -3)

Reorder the terms:
0 = (-3 + 2x)(-3 + 4x)

Multiply (-3 + 2x) * (-3 + 4x)
0 = (-3(-3 + 4x) + 2x * (-3 + 4x))
0 = ((-3 * -3 + 4x * -3) + 2x * (-3 + 4x))
0 = ((9 + -12x) + 2x * (-3 + 4x))
0 = (9 + -12x + (-3 * 2x + 4x * 2x))
0 = (9 + -12x + (-6x + 8x2))

Combine like terms: -12x + -6x = -18x
0 = (9 + -18x + 8x2)

Solving
0 = 9 + -18x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + -9 = -9
-9 + 18x + -8x2 = 9 + -18x + 8x2 + -9 + 18x + -8x2

Reorder the terms:
-9 + 18x + -8x2 = 9 + -9 + -18x + 18x + 8x2 + -8x2

Combine like terms: 9 + -9 = 0
-9 + 18x + -8x2 = 0 + -18x + 18x + 8x2 + -8x2
-9 + 18x + -8x2 = -18x + 18x + 8x2 + -8x2

Combine like terms: -18x + 18x = 0
-9 + 18x + -8x2 = 0 + 8x2 + -8x2
-9 + 18x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
-9 + 18x + -8x2 = 0

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


Subproblem 1
Set the factor '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 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 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5

Subproblem 2
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
Solution
x = {1.5, 0.75}

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