(5x-4)(2x-3)=17

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Solution for (5x-4)(2x-3)=17 equation: 


Simplifying
(5x + -4)(2x + -3) = 17

Reorder the terms:
(-4 + 5x)(2x + -3) = 17

Reorder the terms:
(-4 + 5x)(-3 + 2x) = 17

Multiply (-4 + 5x) * (-3 + 2x)
(-4(-3 + 2x) + 5x * (-3 + 2x)) = 17
((-3 * -4 + 2x * -4) + 5x * (-3 + 2x)) = 17
((12 + -8x) + 5x * (-3 + 2x)) = 17
(12 + -8x + (-3 * 5x + 2x * 5x)) = 17
(12 + -8x + (-15x + 10x2)) = 17

Combine like terms: -8x + -15x = -23x
(12 + -23x + 10x2) = 17

Solving
12 + -23x + 10x2 = 17

Solving for variable 'x'.

Reorder the terms:
12 + -17 + -23x + 10x2 = 17 + -17

Combine like terms: 12 + -17 = -5
-5 + -23x + 10x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-5 + -23x + 10x2 = 0

Factor a trinomial.
(-1 + -5x)(5 + -2x) = 0


Subproblem 1
Set the factor '(-1 + -5x)' equal to zero and attempt to solve:

Simplifying
-1 + -5x = 0

Solving
-1 + -5x = 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 + -5x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5x = 0 + 1
-5x = 0 + 1

Combine like terms: 0 + 1 = 1
-5x = 1

Divide each side by '-5'.
x = -0.2

Simplifying
x = -0.2

Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {-0.2, 2.5}

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