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

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


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

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

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

Multiply (4 + 3x) * (4 + 3x)
(4(4 + 3x) + 3x * (4 + 3x)) = 7(3x + 4)
((4 * 4 + 3x * 4) + 3x * (4 + 3x)) = 7(3x + 4)
((16 + 12x) + 3x * (4 + 3x)) = 7(3x + 4)
(16 + 12x + (4 * 3x + 3x * 3x)) = 7(3x + 4)
(16 + 12x + (12x + 9x2)) = 7(3x + 4)

Combine like terms: 12x + 12x = 24x
(16 + 24x + 9x2) = 7(3x + 4)

Reorder the terms:
16 + 24x + 9x2 = 7(4 + 3x)
16 + 24x + 9x2 = (4 * 7 + 3x * 7)
16 + 24x + 9x2 = (28 + 21x)

Solving
16 + 24x + 9x2 = 28 + 21x

Solving for variable 'x'.

Reorder the terms:
16 + -28 + 24x + -21x + 9x2 = 28 + 21x + -28 + -21x

Combine like terms: 16 + -28 = -12
-12 + 24x + -21x + 9x2 = 28 + 21x + -28 + -21x

Combine like terms: 24x + -21x = 3x
-12 + 3x + 9x2 = 28 + 21x + -28 + -21x

Reorder the terms:
-12 + 3x + 9x2 = 28 + -28 + 21x + -21x

Combine like terms: 28 + -28 = 0
-12 + 3x + 9x2 = 0 + 21x + -21x
-12 + 3x + 9x2 = 21x + -21x

Combine like terms: 21x + -21x = 0
-12 + 3x + 9x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + x + 3x2) = 0

Factor a trinomial.
3((-4 + -3x)(1 + -1x)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-4 + -3x)' equal to zero and attempt to solve: Simplifying -4 + -3x = 0 Solving -4 + -3x = 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 + -3x = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -3x = 0 + 4 -3x = 0 + 4 Combine like terms: 0 + 4 = 4 -3x = 4 Divide each side by '-3'. x = -1.333333333 Simplifying x = -1.333333333

Subproblem 2

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

Solution

x = {-1.333333333, 1}

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