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

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


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

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

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

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

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

Reorder the terms:
-6 + 1x + 7x2 = (-2 + x)(6x + 7)

Reorder the terms:
-6 + 1x + 7x2 = (-2 + x)(7 + 6x)

Multiply (-2 + x) * (7 + 6x)
-6 + 1x + 7x2 = (-2(7 + 6x) + x(7 + 6x))
-6 + 1x + 7x2 = ((7 * -2 + 6x * -2) + x(7 + 6x))
-6 + 1x + 7x2 = ((-14 + -12x) + x(7 + 6x))
-6 + 1x + 7x2 = (-14 + -12x + (7 * x + 6x * x))
-6 + 1x + 7x2 = (-14 + -12x + (7x + 6x2))

Combine like terms: -12x + 7x = -5x
-6 + 1x + 7x2 = (-14 + -5x + 6x2)

Solving
-6 + 1x + 7x2 = -14 + -5x + 6x2

Solving for variable 'x'.

Reorder the terms:
-6 + 14 + 1x + 5x + 7x2 + -6x2 = -14 + -5x + 6x2 + 14 + 5x + -6x2

Combine like terms: -6 + 14 = 8
8 + 1x + 5x + 7x2 + -6x2 = -14 + -5x + 6x2 + 14 + 5x + -6x2

Combine like terms: 1x + 5x = 6x
8 + 6x + 7x2 + -6x2 = -14 + -5x + 6x2 + 14 + 5x + -6x2

Combine like terms: 7x2 + -6x2 = 1x2
8 + 6x + 1x2 = -14 + -5x + 6x2 + 14 + 5x + -6x2

Reorder the terms:
8 + 6x + 1x2 = -14 + 14 + -5x + 5x + 6x2 + -6x2

Combine like terms: -14 + 14 = 0
8 + 6x + 1x2 = 0 + -5x + 5x + 6x2 + -6x2
8 + 6x + 1x2 = -5x + 5x + 6x2 + -6x2

Combine like terms: -5x + 5x = 0
8 + 6x + 1x2 = 0 + 6x2 + -6x2
8 + 6x + 1x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
8 + 6x + 1x2 = 0

Factor a trinomial.
(4 + x)(2 + x) = 0

Subproblem 1

Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4

Subproblem 2

Set the factor '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2

Solution

x = {-4, -2}

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