0=3x^2+x(-5x+4)-x(7x-10)

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Solution for 0=3x^2+x(-5x+4)-x(7x-10) equation: 


Simplifying
0 = 3x2 + x(-5x + 4) + -1x(7x + -10)

Reorder the terms:
0 = 3x2 + x(4 + -5x) + -1x(7x + -10)
0 = 3x2 + (4 * x + -5x * x) + -1x(7x + -10)
0 = 3x2 + (4x + -5x2) + -1x(7x + -10)

Reorder the terms:
0 = 3x2 + 4x + -5x2 + -1x(-10 + 7x)
0 = 3x2 + 4x + -5x2 + (-10 * -1x + 7x * -1x)
0 = 3x2 + 4x + -5x2 + (10x + -7x2)

Reorder the terms:
0 = 4x + 10x + 3x2 + -5x2 + -7x2

Combine like terms: 4x + 10x = 14x
0 = 14x + 3x2 + -5x2 + -7x2

Combine like terms: 3x2 + -5x2 = -2x2
0 = 14x + -2x2 + -7x2

Combine like terms: -2x2 + -7x2 = -9x2
0 = 14x + -9x2

Solving
0 = 14x + -9x2

Solving for variable 'x'.
Remove the zero:
-14x + 9x2 = 14x + -9x2 + -14x + 9x2

Reorder the terms:
-14x + 9x2 = 14x + -14x + -9x2 + 9x2

Combine like terms: 14x + -14x = 0
-14x + 9x2 = 0 + -9x2 + 9x2
-14x + 9x2 = -9x2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-14x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-14 + 9x) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(-14 + 9x)' equal to zero and attempt to solve:

Simplifying
-14 + 9x = 0

Solving
-14 + 9x = 0

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

Add '14' to each side of the equation.
-14 + 14 + 9x = 0 + 14

Combine like terms: -14 + 14 = 0
0 + 9x = 0 + 14
9x = 0 + 14

Combine like terms: 0 + 14 = 14
9x = 14

Divide each side by '9'.
x = 1.555555556

Simplifying
x = 1.555555556
Solution
x = {0, 1.555555556}

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