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

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

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

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

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

Multiply (-3 + x) * (-7 + 4x)
(-3(-7 + 4x) + x(-7 + 4x)) = 0
((-7 * -3 + 4x * -3) + x(-7 + 4x)) = 0
((21 + -12x) + x(-7 + 4x)) = 0
(21 + -12x + (-7 * x + 4x * x)) = 0
(21 + -12x + (-7x + 4x2)) = 0

Combine like terms: -12x + -7x = -19x
(21 + -19x + 4x2) = 0

Solving
21 + -19x + 4x2 = 0

Solving for variable 'x'.

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

Subproblem 1
Set the factor '(7 + -4x)' equal to zero and attempt to solve:

Simplifying
7 + -4x = 0

Solving
7 + -4x = 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 + -4x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -4x = 0 + -7
-4x = 0 + -7

Combine like terms: 0 + -7 = -7
-4x = -7

Divide each side by '-4'.
x = 1.75

Simplifying
x = 1.75
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {1.75, 3}