(x+7)2=(x+7)(3x+4)

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Solution for (x+7)2=(x+7)(3x+4) equation:


Simplifying
(x + 7) * 2 = (x + 7)(3x + 4)

Reorder the terms:
(7 + x) * 2 = (x + 7)(3x + 4)

Reorder the terms for easier multiplication:
2(7 + x) = (x + 7)(3x + 4)
(7 * 2 + x * 2) = (x + 7)(3x + 4)
(14 + 2x) = (x + 7)(3x + 4)

Reorder the terms:
14 + 2x = (7 + x)(3x + 4)

Reorder the terms:
14 + 2x = (7 + x)(4 + 3x)

Multiply (7 + x) * (4 + 3x)
14 + 2x = (7(4 + 3x) + x(4 + 3x))
14 + 2x = ((4 * 7 + 3x * 7) + x(4 + 3x))
14 + 2x = ((28 + 21x) + x(4 + 3x))
14 + 2x = (28 + 21x + (4 * x + 3x * x))
14 + 2x = (28 + 21x + (4x + 3x2))

Combine like terms: 21x + 4x = 25x
14 + 2x = (28 + 25x + 3x2)

Solving
14 + 2x = 28 + 25x + 3x2

Solving for variable 'x'.

Reorder the terms:
14 + -28 + 2x + -25x + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2

Combine like terms: 14 + -28 = -14
-14 + 2x + -25x + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2

Combine like terms: 2x + -25x = -23x
-14 + -23x + -3x2 = 28 + 25x + 3x2 + -28 + -25x + -3x2

Reorder the terms:
-14 + -23x + -3x2 = 28 + -28 + 25x + -25x + 3x2 + -3x2

Combine like terms: 28 + -28 = 0
-14 + -23x + -3x2 = 0 + 25x + -25x + 3x2 + -3x2
-14 + -23x + -3x2 = 25x + -25x + 3x2 + -3x2

Combine like terms: 25x + -25x = 0
-14 + -23x + -3x2 = 0 + 3x2 + -3x2
-14 + -23x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-14 + -23x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(14 + 23x + 3x2) = 0

Factor a trinomial.
-1((7 + x)(2 + 3x)) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(7 + x)' equal to zero and attempt to solve: Simplifying 7 + x = 0 Solving 7 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + x = 0 + -7 x = 0 + -7 Combine like terms: 0 + -7 = -7 x = -7 Simplifying x = -7

Subproblem 2

Set the factor '(2 + 3x)' equal to zero and attempt to solve: Simplifying 2 + 3x = 0 Solving 2 + 3x = 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 + 3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3x = 0 + -2 3x = 0 + -2 Combine like terms: 0 + -2 = -2 3x = -2 Divide each side by '3'. x = -0.6666666667 Simplifying x = -0.6666666667

Solution

x = {-7, -0.6666666667}

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