5x(3x-2)-5x(x+7)+5x(2x+3)=

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Solution for 5x(3x-2)-5x(x+7)+5x(2x+3)= equation: 


Simplifying
5x(3x + -2) + -5x(x + 7) + 5x(2x + 3) = 0

Reorder the terms:
5x(-2 + 3x) + -5x(x + 7) + 5x(2x + 3) = 0
(-2 * 5x + 3x * 5x) + -5x(x + 7) + 5x(2x + 3) = 0
(-10x + 15x2) + -5x(x + 7) + 5x(2x + 3) = 0

Reorder the terms:
-10x + 15x2 + -5x(7 + x) + 5x(2x + 3) = 0
-10x + 15x2 + (7 * -5x + x * -5x) + 5x(2x + 3) = 0
-10x + 15x2 + (-35x + -5x2) + 5x(2x + 3) = 0

Reorder the terms:
-10x + 15x2 + -35x + -5x2 + 5x(3 + 2x) = 0
-10x + 15x2 + -35x + -5x2 + (3 * 5x + 2x * 5x) = 0
-10x + 15x2 + -35x + -5x2 + (15x + 10x2) = 0

Reorder the terms:
-10x + -35x + 15x + 15x2 + -5x2 + 10x2 = 0

Combine like terms: -10x + -35x = -45x
-45x + 15x + 15x2 + -5x2 + 10x2 = 0

Combine like terms: -45x + 15x = -30x
-30x + 15x2 + -5x2 + 10x2 = 0

Combine like terms: 15x2 + -5x2 = 10x2
-30x + 10x2 + 10x2 = 0

Combine like terms: 10x2 + 10x2 = 20x2
-30x + 20x2 = 0

Solving
-30x + 20x2 = 0

Solving for variable 'x'.

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

Ignore the factor 10.

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 '(-3 + 2x)' equal to zero and attempt to solve:

Simplifying
-3 + 2x = 0

Solving
-3 + 2x = 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 + 2x = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {0, 1.5}

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