(2x+9)(x-3)=-19(x-7)

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Solution for (2x+9)(x-3)=-19(x-7) equation: 


Simplifying
(2x + 9)(x + -3) = -19(x + -7)

Reorder the terms:
(9 + 2x)(x + -3) = -19(x + -7)

Reorder the terms:
(9 + 2x)(-3 + x) = -19(x + -7)

Multiply (9 + 2x) * (-3 + x)
(9(-3 + x) + 2x * (-3 + x)) = -19(x + -7)
((-3 * 9 + x * 9) + 2x * (-3 + x)) = -19(x + -7)
((-27 + 9x) + 2x * (-3 + x)) = -19(x + -7)
(-27 + 9x + (-3 * 2x + x * 2x)) = -19(x + -7)
(-27 + 9x + (-6x + 2x2)) = -19(x + -7)

Combine like terms: 9x + -6x = 3x
(-27 + 3x + 2x2) = -19(x + -7)

Reorder the terms:
-27 + 3x + 2x2 = -19(-7 + x)
-27 + 3x + 2x2 = (-7 * -19 + x * -19)
-27 + 3x + 2x2 = (133 + -19x)

Solving
-27 + 3x + 2x2 = 133 + -19x

Solving for variable 'x'.

Reorder the terms:
-27 + -133 + 3x + 19x + 2x2 = 133 + -19x + -133 + 19x

Combine like terms: -27 + -133 = -160
-160 + 3x + 19x + 2x2 = 133 + -19x + -133 + 19x

Combine like terms: 3x + 19x = 22x
-160 + 22x + 2x2 = 133 + -19x + -133 + 19x

Reorder the terms:
-160 + 22x + 2x2 = 133 + -133 + -19x + 19x

Combine like terms: 133 + -133 = 0
-160 + 22x + 2x2 = 0 + -19x + 19x
-160 + 22x + 2x2 = -19x + 19x

Combine like terms: -19x + 19x = 0
-160 + 22x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-80 + 11x + x2) = 0

Factor a trinomial.
2((-16 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-16 + -1x)' equal to zero and attempt to solve:

Simplifying
-16 + -1x = 0

Solving
-16 + -1x = 0

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

Add '16' to each side of the equation.
-16 + 16 + -1x = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -1x = 0 + 16
-1x = 0 + 16

Combine like terms: 0 + 16 = 16
-1x = 16

Divide each side by '-1'.
x = -16

Simplifying
x = -16

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-16, 5}

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