(7x+3)(x-5)=-2x(5x+6)+x-19

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Solution for (7x+3)(x-5)=-2x(5x+6)+x-19 equation:


Simplifying
(7x + 3)(x + -5) = -2x(5x + 6) + x + -19

Reorder the terms:
(3 + 7x)(x + -5) = -2x(5x + 6) + x + -19

Reorder the terms:
(3 + 7x)(-5 + x) = -2x(5x + 6) + x + -19

Multiply (3 + 7x) * (-5 + x)
(3(-5 + x) + 7x * (-5 + x)) = -2x(5x + 6) + x + -19
((-5 * 3 + x * 3) + 7x * (-5 + x)) = -2x(5x + 6) + x + -19
((-15 + 3x) + 7x * (-5 + x)) = -2x(5x + 6) + x + -19
(-15 + 3x + (-5 * 7x + x * 7x)) = -2x(5x + 6) + x + -19
(-15 + 3x + (-35x + 7x2)) = -2x(5x + 6) + x + -19

Combine like terms: 3x + -35x = -32x
(-15 + -32x + 7x2) = -2x(5x + 6) + x + -19

Reorder the terms:
-15 + -32x + 7x2 = -2x(6 + 5x) + x + -19
-15 + -32x + 7x2 = (6 * -2x + 5x * -2x) + x + -19
-15 + -32x + 7x2 = (-12x + -10x2) + x + -19

Reorder the terms:
-15 + -32x + 7x2 = -19 + -12x + x + -10x2

Combine like terms: -12x + x = -11x
-15 + -32x + 7x2 = -19 + -11x + -10x2

Solving
-15 + -32x + 7x2 = -19 + -11x + -10x2

Solving for variable 'x'.

Reorder the terms:
-15 + 19 + -32x + 11x + 7x2 + 10x2 = -19 + -11x + -10x2 + 19 + 11x + 10x2

Combine like terms: -15 + 19 = 4
4 + -32x + 11x + 7x2 + 10x2 = -19 + -11x + -10x2 + 19 + 11x + 10x2

Combine like terms: -32x + 11x = -21x
4 + -21x + 7x2 + 10x2 = -19 + -11x + -10x2 + 19 + 11x + 10x2

Combine like terms: 7x2 + 10x2 = 17x2
4 + -21x + 17x2 = -19 + -11x + -10x2 + 19 + 11x + 10x2

Reorder the terms:
4 + -21x + 17x2 = -19 + 19 + -11x + 11x + -10x2 + 10x2

Combine like terms: -19 + 19 = 0
4 + -21x + 17x2 = 0 + -11x + 11x + -10x2 + 10x2
4 + -21x + 17x2 = -11x + 11x + -10x2 + 10x2

Combine like terms: -11x + 11x = 0
4 + -21x + 17x2 = 0 + -10x2 + 10x2
4 + -21x + 17x2 = -10x2 + 10x2

Combine like terms: -10x2 + 10x2 = 0
4 + -21x + 17x2 = 0

Factor a trinomial.
(4 + -17x)(1 + -1x) = 0


Subproblem 1
Set the factor '(4 + -17x)' equal to zero and attempt to solve:

Simplifying
4 + -17x = 0

Solving
4 + -17x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -17x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -17x = 0 + -4
-17x = 0 + -4

Combine like terms: 0 + -4 = -4
-17x = -4

Divide each side by '-17'.
x = 0.2352941176

Simplifying
x = 0.2352941176

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 = {0.2352941176, 1}

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