(5x-6)(x-1)-(2x-5x+3)=0

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Solution for (5x-6)(x-1)-(2x-5x+3)=0 equation:


Simplifying
(5x + -6)(x + -1) + -1(2x + -5x + 3) = 0

Reorder the terms:
(-6 + 5x)(x + -1) + -1(2x + -5x + 3) = 0

Reorder the terms:
(-6 + 5x)(-1 + x) + -1(2x + -5x + 3) = 0

Multiply (-6 + 5x) * (-1 + x)
(-6(-1 + x) + 5x * (-1 + x)) + -1(2x + -5x + 3) = 0
((-1 * -6 + x * -6) + 5x * (-1 + x)) + -1(2x + -5x + 3) = 0
((6 + -6x) + 5x * (-1 + x)) + -1(2x + -5x + 3) = 0
(6 + -6x + (-1 * 5x + x * 5x)) + -1(2x + -5x + 3) = 0
(6 + -6x + (-5x + 5x2)) + -1(2x + -5x + 3) = 0

Combine like terms: -6x + -5x = -11x
(6 + -11x + 5x2) + -1(2x + -5x + 3) = 0

Reorder the terms:
6 + -11x + 5x2 + -1(3 + 2x + -5x) = 0

Combine like terms: 2x + -5x = -3x
6 + -11x + 5x2 + -1(3 + -3x) = 0
6 + -11x + 5x2 + (3 * -1 + -3x * -1) = 0
6 + -11x + 5x2 + (-3 + 3x) = 0

Reorder the terms:
6 + -3 + -11x + 3x + 5x2 = 0

Combine like terms: 6 + -3 = 3
3 + -11x + 3x + 5x2 = 0

Combine like terms: -11x + 3x = -8x
3 + -8x + 5x2 = 0

Solving
3 + -8x + 5x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + -5x)(1 + -1x) = 0

Subproblem 1

Set the factor '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6

Subproblem 2

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

Solution

x = {0.6, 1}

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