(x-4)(5x-2)-3(x-4)=0

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Solution for (x-4)(5x-2)-3(x-4)=0 equation: 


Simplifying
(x + -4)(5x + -2) + -3(x + -4) = 0

Reorder the terms:
(-4 + x)(5x + -2) + -3(x + -4) = 0

Reorder the terms:
(-4 + x)(-2 + 5x) + -3(x + -4) = 0

Multiply (-4 + x) * (-2 + 5x)
(-4(-2 + 5x) + x(-2 + 5x)) + -3(x + -4) = 0
((-2 * -4 + 5x * -4) + x(-2 + 5x)) + -3(x + -4) = 0
((8 + -20x) + x(-2 + 5x)) + -3(x + -4) = 0
(8 + -20x + (-2 * x + 5x * x)) + -3(x + -4) = 0
(8 + -20x + (-2x + 5x2)) + -3(x + -4) = 0

Combine like terms: -20x + -2x = -22x
(8 + -22x + 5x2) + -3(x + -4) = 0

Reorder the terms:
8 + -22x + 5x2 + -3(-4 + x) = 0
8 + -22x + 5x2 + (-4 * -3 + x * -3) = 0
8 + -22x + 5x2 + (12 + -3x) = 0

Reorder the terms:
8 + 12 + -22x + -3x + 5x2 = 0

Combine like terms: 8 + 12 = 20
20 + -22x + -3x + 5x2 = 0

Combine like terms: -22x + -3x = -25x
20 + -25x + 5x2 = 0

Solving
20 + -25x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(4 + -5x + x2) = 0

Factor a trinomial.
5((1 + -1x)(4 + -1x)) = 0

Ignore the factor 5.

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

Simplifying
1 + -1x = 0

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

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

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

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

Simplifying
x = 1

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, 4}

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