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

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


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

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

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

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

Multiply (2 + x) * (2 + x)
7 + 6x = (2(2 + x) + x(2 + x))
7 + 6x = ((2 * 2 + x * 2) + x(2 + x))
7 + 6x = ((4 + 2x) + x(2 + x))
7 + 6x = (4 + 2x + (2 * x + x * x))
7 + 6x = (4 + 2x + (2x + x2))

Combine like terms: 2x + 2x = 4x
7 + 6x = (4 + 4x + x2)

Solving
7 + 6x = 4 + 4x + x2

Solving for variable 'x'.

Reorder the terms:
7 + -4 + 6x + -4x + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 7 + -4 = 3
3 + 6x + -4x + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Combine like terms: 6x + -4x = 2x
3 + 2x + -1x2 = 4 + 4x + x2 + -4 + -4x + -1x2

Reorder the terms:
3 + 2x + -1x2 = 4 + -4 + 4x + -4x + x2 + -1x2

Combine like terms: 4 + -4 = 0
3 + 2x + -1x2 = 0 + 4x + -4x + x2 + -1x2
3 + 2x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
3 + 2x + -1x2 = 0 + x2 + -1x2
3 + 2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 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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