(3x+2)(x-3)=7(x-1)+6

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Solution for (3x+2)(x-3)=7(x-1)+6 equation:


Simplifying
(3x + 2)(x + -3) = 7(x + -1) + 6

Reorder the terms:
(2 + 3x)(x + -3) = 7(x + -1) + 6

Reorder the terms:
(2 + 3x)(-3 + x) = 7(x + -1) + 6

Multiply (2 + 3x) * (-3 + x)
(2(-3 + x) + 3x * (-3 + x)) = 7(x + -1) + 6
((-3 * 2 + x * 2) + 3x * (-3 + x)) = 7(x + -1) + 6
((-6 + 2x) + 3x * (-3 + x)) = 7(x + -1) + 6
(-6 + 2x + (-3 * 3x + x * 3x)) = 7(x + -1) + 6
(-6 + 2x + (-9x + 3x2)) = 7(x + -1) + 6

Combine like terms: 2x + -9x = -7x
(-6 + -7x + 3x2) = 7(x + -1) + 6

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

Reorder the terms:
-6 + -7x + 3x2 = -7 + 6 + 7x

Combine like terms: -7 + 6 = -1
-6 + -7x + 3x2 = -1 + 7x

Solving
-6 + -7x + 3x2 = -1 + 7x

Solving for variable 'x'.

Reorder the terms:
-6 + 1 + -7x + -7x + 3x2 = -1 + 7x + 1 + -7x

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

Combine like terms: -7x + -7x = -14x
-5 + -14x + 3x2 = -1 + 7x + 1 + -7x

Reorder the terms:
-5 + -14x + 3x2 = -1 + 1 + 7x + -7x

Combine like terms: -1 + 1 = 0
-5 + -14x + 3x2 = 0 + 7x + -7x
-5 + -14x + 3x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
-5 + -14x + 3x2 = 0

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

Subproblem 1

Set the factor '(-1 + -3x)' equal to zero and attempt to solve: Simplifying -1 + -3x = 0 Solving -1 + -3x = 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 + -3x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3x = 0 + 1 -3x = 0 + 1 Combine like terms: 0 + 1 = 1 -3x = 1 Divide each side by '-3'. x = -0.3333333333 Simplifying x = -0.3333333333

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 = {-0.3333333333, 5}

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