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

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

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

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

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

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

Solving
-12 + 25x + 7x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

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

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

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(3 + -7x)' equal to zero and attempt to solve:

Simplifying
3 + -7x = 0

Solving
3 + -7x = 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 + -7x = 0 + -3

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

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

Divide each side by '-7'.
x = 0.4285714286

Simplifying
x = 0.4285714286
Solution
x = {-4, 0.4285714286}