(-7x+3)(x-6)=0

Solution for (-7x+3)(x-6)=0 equation:

Simplifying
(-7x + 3)(x + -6) = 0

Reorder the terms:
(3 + -7x)(x + -6) = 0

Reorder the terms:
(3 + -7x)(-6 + x) = 0

Multiply (3 + -7x) * (-6 + x)
(3(-6 + x) + -7x * (-6 + x)) = 0
((-6 * 3 + x * 3) + -7x * (-6 + x)) = 0
((-18 + 3x) + -7x * (-6 + x)) = 0
(-18 + 3x + (-6 * -7x + x * -7x)) = 0
(-18 + 3x + (42x + -7x2)) = 0

Combine like terms: 3x + 42x = 45x
(-18 + 45x + -7x2) = 0

Solving
-18 + 45x + -7x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6 + x)(3 + -7x) = 0

Subproblem 1
Set the factor '(-6 + x)' equal to zero and attempt to solve:

Simplifying
-6 + x = 0

Solving
-6 + x = 0

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

Add '6' to each side of the equation.
-6 + 6 + x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + x = 0 + 6
x = 0 + 6

Combine like terms: 0 + 6 = 6
x = 6

Simplifying
x = 6
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 = {6, 0.4285714286}