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

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


Simplifying
x + -1(4 + -3x)(2x + -5) = 0

Reorder the terms:
x + -1(4 + -3x)(-5 + 2x) = 0

Multiply (4 + -3x) * (-5 + 2x)
x + -1(4(-5 + 2x) + -3x * (-5 + 2x)) = 0
x + -1((-5 * 4 + 2x * 4) + -3x * (-5 + 2x)) = 0
x + -1((-20 + 8x) + -3x * (-5 + 2x)) = 0
x + -1(-20 + 8x + (-5 * -3x + 2x * -3x)) = 0
x + -1(-20 + 8x + (15x + -6x2)) = 0

Combine like terms: 8x + 15x = 23x
x + -1(-20 + 23x + -6x2) = 0
x + (-20 * -1 + 23x * -1 + -6x2 * -1) = 0
x + (20 + -23x + 6x2) = 0

Reorder the terms:
20 + x + -23x + 6x2 = 0

Combine like terms: x + -23x = -22x
20 + -22x + 6x2 = 0

Solving
20 + -22x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(10 + -11x + 3x2) = 0

Factor a trinomial.
2((5 + -3x)(2 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -3x)' equal to zero and attempt to solve:

Simplifying
5 + -3x = 0

Solving
5 + -3x = 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 + -3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3x = 0 + -5
-3x = 0 + -5

Combine like terms: 0 + -5 = -5
-3x = -5

Divide each side by '-3'.
x = 1.666666667

Simplifying
x = 1.666666667

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1.666666667, 2}

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