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

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


Simplifying
5(x + -2) + -3(2 + -1x)(x + 7) = 0

Reorder the terms:
5(-2 + x) + -3(2 + -1x)(x + 7) = 0
(-2 * 5 + x * 5) + -3(2 + -1x)(x + 7) = 0
(-10 + 5x) + -3(2 + -1x)(x + 7) = 0

Reorder the terms:
-10 + 5x + -3(2 + -1x)(7 + x) = 0

Multiply (2 + -1x) * (7 + x)
-10 + 5x + -3(2(7 + x) + -1x * (7 + x)) = 0
-10 + 5x + -3((7 * 2 + x * 2) + -1x * (7 + x)) = 0
-10 + 5x + -3((14 + 2x) + -1x * (7 + x)) = 0
-10 + 5x + -3(14 + 2x + (7 * -1x + x * -1x)) = 0
-10 + 5x + -3(14 + 2x + (-7x + -1x2)) = 0

Combine like terms: 2x + -7x = -5x
-10 + 5x + -3(14 + -5x + -1x2) = 0
-10 + 5x + (14 * -3 + -5x * -3 + -1x2 * -3) = 0
-10 + 5x + (-42 + 15x + 3x2) = 0

Reorder the terms:
-10 + -42 + 5x + 15x + 3x2 = 0

Combine like terms: -10 + -42 = -52
-52 + 5x + 15x + 3x2 = 0

Combine like terms: 5x + 15x = 20x
-52 + 20x + 3x2 = 0

Solving
-52 + 20x + 3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-26 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-26 + -3x)' equal to zero and attempt to solve:

Simplifying
-26 + -3x = 0

Solving
-26 + -3x = 0

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

Add '26' to each side of the equation.
-26 + 26 + -3x = 0 + 26

Combine like terms: -26 + 26 = 0
0 + -3x = 0 + 26
-3x = 0 + 26

Combine like terms: 0 + 26 = 26
-3x = 26

Divide each side by '-3'.
x = -8.666666667

Simplifying
x = -8.666666667

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 = {-8.666666667, 2}

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