(5x-2)(x-3)=-17x+10

Solution for (5x-2)(x-3)=-17x+10 equation:

Simplifying
(5x + -2)(x + -3) = -17x + 10

Reorder the terms:
(-2 + 5x)(x + -3) = -17x + 10

Reorder the terms:
(-2 + 5x)(-3 + x) = -17x + 10

Multiply (-2 + 5x) * (-3 + x)
(-2(-3 + x) + 5x * (-3 + x)) = -17x + 10
((-3 * -2 + x * -2) + 5x * (-3 + x)) = -17x + 10
((6 + -2x) + 5x * (-3 + x)) = -17x + 10
(6 + -2x + (-3 * 5x + x * 5x)) = -17x + 10
(6 + -2x + (-15x + 5x2)) = -17x + 10

Combine like terms: -2x + -15x = -17x
(6 + -17x + 5x2) = -17x + 10

Reorder the terms:
6 + -17x + 5x2 = 10 + -17x

Add '17x' to each side of the equation.
6 + -17x + 17x + 5x2 = 10 + -17x + 17x

Combine like terms: -17x + 17x = 0
6 + 0 + 5x2 = 10 + -17x + 17x
6 + 5x2 = 10 + -17x + 17x

Combine like terms: -17x + 17x = 0
6 + 5x2 = 10 + 0
6 + 5x2 = 10

Solving
6 + 5x2 = 10

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + 5x2 = 10 + -6

Combine like terms: 6 + -6 = 0
0 + 5x2 = 10 + -6
5x2 = 10 + -6

Combine like terms: 10 + -6 = 4
5x2 = 4

Divide each side by '5'.
x2 = 0.8

Simplifying
x2 = 0.8

Take the square root of each side:
x = {-0.894427191, 0.894427191}