(7x+2)(7x+2)+6(7x+2)=27

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Solution for (7x+2)(7x+2)+6(7x+2)=27 equation:


Simplifying
(7x + 2)(7x + 2) + 6(7x + 2) = 27

Reorder the terms:
(2 + 7x)(7x + 2) + 6(7x + 2) = 27

Reorder the terms:
(2 + 7x)(2 + 7x) + 6(7x + 2) = 27

Multiply (2 + 7x) * (2 + 7x)
(2(2 + 7x) + 7x * (2 + 7x)) + 6(7x + 2) = 27
((2 * 2 + 7x * 2) + 7x * (2 + 7x)) + 6(7x + 2) = 27
((4 + 14x) + 7x * (2 + 7x)) + 6(7x + 2) = 27
(4 + 14x + (2 * 7x + 7x * 7x)) + 6(7x + 2) = 27
(4 + 14x + (14x + 49x2)) + 6(7x + 2) = 27

Combine like terms: 14x + 14x = 28x
(4 + 28x + 49x2) + 6(7x + 2) = 27

Reorder the terms:
4 + 28x + 49x2 + 6(2 + 7x) = 27
4 + 28x + 49x2 + (2 * 6 + 7x * 6) = 27
4 + 28x + 49x2 + (12 + 42x) = 27

Reorder the terms:
4 + 12 + 28x + 42x + 49x2 = 27

Combine like terms: 4 + 12 = 16
16 + 28x + 42x + 49x2 = 27

Combine like terms: 28x + 42x = 70x
16 + 70x + 49x2 = 27

Solving
16 + 70x + 49x2 = 27

Solving for variable 'x'.

Reorder the terms:
16 + -27 + 70x + 49x2 = 27 + -27

Combine like terms: 16 + -27 = -11
-11 + 70x + 49x2 = 27 + -27

Combine like terms: 27 + -27 = 0
-11 + 70x + 49x2 = 0

Factor a trinomial.
(-11 + -7x)(1 + -7x) = 0

Subproblem 1

Set the factor '(-11 + -7x)' equal to zero and attempt to solve: Simplifying -11 + -7x = 0 Solving -11 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -7x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -7x = 0 + 11 -7x = 0 + 11 Combine like terms: 0 + 11 = 11 -7x = 11 Divide each side by '-7'. x = -1.571428571 Simplifying x = -1.571428571

Subproblem 2

Set the factor '(1 + -7x)' equal to zero and attempt to solve: Simplifying 1 + -7x = 0 Solving 1 + -7x = 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 + -7x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -7x = 0 + -1 -7x = 0 + -1 Combine like terms: 0 + -1 = -1 -7x = -1 Divide each side by '-7'. x = 0.1428571429 Simplifying x = 0.1428571429

Solution

x = {-1.571428571, 0.1428571429}

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