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

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


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

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

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

Multiply (6 + x) * (-3 + x)
(6(-3 + x) + x(-3 + x)) = (2x + 7)(x + -3)
((-3 * 6 + x * 6) + x(-3 + x)) = (2x + 7)(x + -3)
((-18 + 6x) + x(-3 + x)) = (2x + 7)(x + -3)
(-18 + 6x + (-3 * x + x * x)) = (2x + 7)(x + -3)
(-18 + 6x + (-3x + x2)) = (2x + 7)(x + -3)

Combine like terms: 6x + -3x = 3x
(-18 + 3x + x2) = (2x + 7)(x + -3)

Reorder the terms:
-18 + 3x + x2 = (7 + 2x)(x + -3)

Reorder the terms:
-18 + 3x + x2 = (7 + 2x)(-3 + x)

Multiply (7 + 2x) * (-3 + x)
-18 + 3x + x2 = (7(-3 + x) + 2x * (-3 + x))
-18 + 3x + x2 = ((-3 * 7 + x * 7) + 2x * (-3 + x))
-18 + 3x + x2 = ((-21 + 7x) + 2x * (-3 + x))
-18 + 3x + x2 = (-21 + 7x + (-3 * 2x + x * 2x))
-18 + 3x + x2 = (-21 + 7x + (-6x + 2x2))

Combine like terms: 7x + -6x = 1x
-18 + 3x + x2 = (-21 + 1x + 2x2)

Solving
-18 + 3x + x2 = -21 + 1x + 2x2

Solving for variable 'x'.

Reorder the terms:
-18 + 21 + 3x + -1x + x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2

Combine like terms: -18 + 21 = 3
3 + 3x + -1x + x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2

Combine like terms: 3x + -1x = 2x
3 + 2x + x2 + -2x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2

Combine like terms: x2 + -2x2 = -1x2
3 + 2x + -1x2 = -21 + 1x + 2x2 + 21 + -1x + -2x2

Reorder the terms:
3 + 2x + -1x2 = -21 + 21 + 1x + -1x + 2x2 + -2x2

Combine like terms: -21 + 21 = 0
3 + 2x + -1x2 = 0 + 1x + -1x + 2x2 + -2x2
3 + 2x + -1x2 = 1x + -1x + 2x2 + -2x2

Combine like terms: 1x + -1x = 0
3 + 2x + -1x2 = 0 + 2x2 + -2x2
3 + 2x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
3 + 2x + -1x2 = 0

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

Subproblem 1

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Subproblem 2

Set the factor '(1 + x)' equal to zero and attempt to solve: Simplifying 1 + x = 0 Solving 1 + x = 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 + x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + x = 0 + -1 x = 0 + -1 Combine like terms: 0 + -1 = -1 x = -1 Simplifying x = -1

Solution

x = {3, -1}

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