=(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 = 6x
0 = (-9 + 6x + 8x2)

Solving
0 = -9 + 6x + 8x2

Solving for variable 'x'.

Combine like terms: 0 + 9 = 9
9 + -6x + -8x2 = -9 + 6x + 8x2 + 9 + -6x + -8x2

Reorder the terms:
9 + -6x + -8x2 = -9 + 9 + 6x + -6x + 8x2 + -8x2

Combine like terms: -9 + 9 = 0
9 + -6x + -8x2 = 0 + 6x + -6x + 8x2 + -8x2
9 + -6x + -8x2 = 6x + -6x + 8x2 + -8x2

Combine like terms: 6x + -6x = 0
9 + -6x + -8x2 = 0 + 8x2 + -8x2
9 + -6x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
9 + -6x + -8x2 = 0

Factor a trinomial.
(3 + -4x)(3 + 2x) = 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 '(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
Solution
x = {0.75, -1.5}

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