3x(2x-5)-(x+7)=(x-9)(-5)

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Solution for 3x(2x-5)-(x+7)=(x-9)(-5) equation: 


Simplifying
3x(2x + -5) + -1(x + 7) = (x + -9)(-5)

Reorder the terms:
3x(-5 + 2x) + -1(x + 7) = (x + -9)(-5)
(-5 * 3x + 2x * 3x) + -1(x + 7) = (x + -9)(-5)
(-15x + 6x2) + -1(x + 7) = (x + -9)(-5)

Reorder the terms:
-15x + 6x2 + -1(7 + x) = (x + -9)(-5)
-15x + 6x2 + (7 * -1 + x * -1) = (x + -9)(-5)
-15x + 6x2 + (-7 + -1x) = (x + -9)(-5)

Reorder the terms:
-7 + -15x + -1x + 6x2 = (x + -9)(-5)

Combine like terms: -15x + -1x = -16x
-7 + -16x + 6x2 = (x + -9)(-5)

Reorder the terms:
-7 + -16x + 6x2 = (-9 + x)(-5)

Reorder the terms for easier multiplication:
-7 + -16x + 6x2 = -5(-9 + x)
-7 + -16x + 6x2 = (-9 * -5 + x * -5)
-7 + -16x + 6x2 = (45 + -5x)

Solving
-7 + -16x + 6x2 = 45 + -5x

Solving for variable 'x'.

Reorder the terms:
-7 + -45 + -16x + 5x + 6x2 = 45 + -5x + -45 + 5x

Combine like terms: -7 + -45 = -52
-52 + -16x + 5x + 6x2 = 45 + -5x + -45 + 5x

Combine like terms: -16x + 5x = -11x
-52 + -11x + 6x2 = 45 + -5x + -45 + 5x

Reorder the terms:
-52 + -11x + 6x2 = 45 + -45 + -5x + 5x

Combine like terms: 45 + -45 = 0
-52 + -11x + 6x2 = 0 + -5x + 5x
-52 + -11x + 6x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
-52 + -11x + 6x2 = 0

Factor a trinomial.
(-13 + -6x)(4 + -1x) = 0


Subproblem 1
Set the factor '(-13 + -6x)' equal to zero and attempt to solve:

Simplifying
-13 + -6x = 0

Solving
-13 + -6x = 0

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

Add '13' to each side of the equation.
-13 + 13 + -6x = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -6x = 0 + 13
-6x = 0 + 13

Combine like terms: 0 + 13 = 13
-6x = 13

Divide each side by '-6'.
x = -2.166666667

Simplifying
x = -2.166666667

Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Solution
x = {-2.166666667, 4}

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