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

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


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

Reorder the terms:
3x(-5 + x) + 7x = -1(5 + 3x2) + 5x
(-5 * 3x + x * 3x) + 7x = -1(5 + 3x2) + 5x
(-15x + 3x2) + 7x = -1(5 + 3x2) + 5x

Reorder the terms:
-15x + 7x + 3x2 = -1(5 + 3x2) + 5x

Combine like terms: -15x + 7x = -8x
-8x + 3x2 = -1(5 + 3x2) + 5x
-8x + 3x2 = (5 * -1 + 3x2 * -1) + 5x
-8x + 3x2 = (-5 + -3x2) + 5x

Reorder the terms:
-8x + 3x2 = -5 + 5x + -3x2

Solving
-8x + 3x2 = -5 + 5x + -3x2

Solving for variable 'x'.

Reorder the terms:
5 + -8x + -5x + 3x2 + 3x2 = -5 + 5x + -3x2 + 5 + -5x + 3x2

Combine like terms: -8x + -5x = -13x
5 + -13x + 3x2 + 3x2 = -5 + 5x + -3x2 + 5 + -5x + 3x2

Combine like terms: 3x2 + 3x2 = 6x2
5 + -13x + 6x2 = -5 + 5x + -3x2 + 5 + -5x + 3x2

Reorder the terms:
5 + -13x + 6x2 = -5 + 5 + 5x + -5x + -3x2 + 3x2

Combine like terms: -5 + 5 = 0
5 + -13x + 6x2 = 0 + 5x + -5x + -3x2 + 3x2
5 + -13x + 6x2 = 5x + -5x + -3x2 + 3x2

Combine like terms: 5x + -5x = 0
5 + -13x + 6x2 = 0 + -3x2 + 3x2
5 + -13x + 6x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
5 + -13x + 6x2 = 0

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


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 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 + -2x = 0 + -1

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
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
Solution
x = {0.5, 1.666666667}

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