(5x-3)(x-2)=34

Solution for (5x-3)(x-2)=34 equation:

Simplifying
(5x + -3)(x + -2) = 34

Reorder the terms:
(-3 + 5x)(x + -2) = 34

Reorder the terms:
(-3 + 5x)(-2 + x) = 34

Multiply (-3 + 5x) * (-2 + x)
(-3(-2 + x) + 5x * (-2 + x)) = 34
((-2 * -3 + x * -3) + 5x * (-2 + x)) = 34
((6 + -3x) + 5x * (-2 + x)) = 34
(6 + -3x + (-2 * 5x + x * 5x)) = 34
(6 + -3x + (-10x + 5x2)) = 34

Combine like terms: -3x + -10x = -13x
(6 + -13x + 5x2) = 34

Solving
6 + -13x + 5x2 = 34

Solving for variable 'x'.

Reorder the terms:
6 + -34 + -13x + 5x2 = 34 + -34

Combine like terms: 6 + -34 = -28
-28 + -13x + 5x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-28 + -13x + 5x2 = 0

Factor a trinomial.
(-7 + -5x)(4 + -1x) = 0

Subproblem 1
Set the factor '(-7 + -5x)' equal to zero and attempt to solve:

Simplifying
-7 + -5x = 0

Solving
-7 + -5x = 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 + -5x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -5x = 0 + 7
-5x = 0 + 7

Combine like terms: 0 + 7 = 7
-5x = 7

Divide each side by '-5'.
x = -1.4

Simplifying
x = -1.4
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, 4}