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

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


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

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

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

Multiply (-4 + x) * (-7 + 4x)
(-4(-7 + 4x) + x(-7 + 4x)) = 0
((-7 * -4 + 4x * -4) + x(-7 + 4x)) = 0
((28 + -16x) + x(-7 + 4x)) = 0
(28 + -16x + (-7 * x + 4x * x)) = 0
(28 + -16x + (-7x + 4x2)) = 0

Combine like terms: -16x + -7x = -23x
(28 + -23x + 4x2) = 0

Solving
28 + -23x + 4x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + -4x)(4 + -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 '(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
Solution
x = {1.75, 4}

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