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

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


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

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

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

Multiply (-5 + 3x) * (2 + x)
(-5(2 + x) + 3x * (2 + x)) = -7(3x + -5)
((2 * -5 + x * -5) + 3x * (2 + x)) = -7(3x + -5)
((-10 + -5x) + 3x * (2 + x)) = -7(3x + -5)
(-10 + -5x + (2 * 3x + x * 3x)) = -7(3x + -5)
(-10 + -5x + (6x + 3x2)) = -7(3x + -5)

Combine like terms: -5x + 6x = 1x
(-10 + 1x + 3x2) = -7(3x + -5)

Reorder the terms:
-10 + 1x + 3x2 = -7(-5 + 3x)
-10 + 1x + 3x2 = (-5 * -7 + 3x * -7)
-10 + 1x + 3x2 = (35 + -21x)

Solving
-10 + 1x + 3x2 = 35 + -21x

Solving for variable 'x'.

Reorder the terms:
-10 + -35 + 1x + 21x + 3x2 = 35 + -21x + -35 + 21x

Combine like terms: -10 + -35 = -45
-45 + 1x + 21x + 3x2 = 35 + -21x + -35 + 21x

Combine like terms: 1x + 21x = 22x
-45 + 22x + 3x2 = 35 + -21x + -35 + 21x

Reorder the terms:
-45 + 22x + 3x2 = 35 + -35 + -21x + 21x

Combine like terms: 35 + -35 = 0
-45 + 22x + 3x2 = 0 + -21x + 21x
-45 + 22x + 3x2 = -21x + 21x

Combine like terms: -21x + 21x = 0
-45 + 22x + 3x2 = 0

Factor a trinomial.
(-9 + -1x)(5 + -3x) = 0


Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

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 = {-9, 1.666666667}

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