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

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


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

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

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

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

Combine like terms: 6x + -12x = -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 + -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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