0=(3x+7)(4x-1)

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Solution for 0=(3x+7)(4x-1) equation: 


Simplifying
0 = (3x + 7)(4x + -1)

Reorder the terms:
0 = (7 + 3x)(4x + -1)

Reorder the terms:
0 = (7 + 3x)(-1 + 4x)

Multiply (7 + 3x) * (-1 + 4x)
0 = (7(-1 + 4x) + 3x * (-1 + 4x))
0 = ((-1 * 7 + 4x * 7) + 3x * (-1 + 4x))
0 = ((-7 + 28x) + 3x * (-1 + 4x))
0 = (-7 + 28x + (-1 * 3x + 4x * 3x))
0 = (-7 + 28x + (-3x + 12x2))

Combine like terms: 28x + -3x = 25x
0 = (-7 + 25x + 12x2)

Solving
0 = -7 + 25x + 12x2

Solving for variable 'x'.

Combine like terms: 0 + 7 = 7
7 + -25x + -12x2 = -7 + 25x + 12x2 + 7 + -25x + -12x2

Reorder the terms:
7 + -25x + -12x2 = -7 + 7 + 25x + -25x + 12x2 + -12x2

Combine like terms: -7 + 7 = 0
7 + -25x + -12x2 = 0 + 25x + -25x + 12x2 + -12x2
7 + -25x + -12x2 = 25x + -25x + 12x2 + -12x2

Combine like terms: 25x + -25x = 0
7 + -25x + -12x2 = 0 + 12x2 + -12x2
7 + -25x + -12x2 = 12x2 + -12x2

Combine like terms: 12x2 + -12x2 = 0
7 + -25x + -12x2 = 0

Factor a trinomial.
(1 + -4x)(7 + 3x) = 0


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

Simplifying
1 + -4x = 0

Solving
1 + -4x = 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 + -4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4x = 0 + -1
-4x = 0 + -1

Combine like terms: 0 + -1 = -1
-4x = -1

Divide each side by '-4'.
x = 0.25

Simplifying
x = 0.25

Subproblem 2
Set the factor '(7 + 3x)' equal to zero and attempt to solve:

Simplifying
7 + 3x = 0

Solving
7 + 3x = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3x = 0 + -7
3x = 0 + -7

Combine like terms: 0 + -7 = -7
3x = -7

Divide each side by '3'.
x = -2.333333333

Simplifying
x = -2.333333333
Solution
x = {0.25, -2.333333333}

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