7(x+1)(x+1)-62(x+1)=9

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Solution for 7(x+1)(x+1)-62(x+1)=9 equation:


Simplifying
7(x + 1)(x + 1) + -62(x + 1) = 9

Reorder the terms:
7(1 + x)(x + 1) + -62(x + 1) = 9

Reorder the terms:
7(1 + x)(1 + x) + -62(x + 1) = 9

Multiply (1 + x) * (1 + x)
7(1(1 + x) + x(1 + x)) + -62(x + 1) = 9
7((1 * 1 + x * 1) + x(1 + x)) + -62(x + 1) = 9
7((1 + 1x) + x(1 + x)) + -62(x + 1) = 9
7(1 + 1x + (1 * x + x * x)) + -62(x + 1) = 9
7(1 + 1x + (1x + x2)) + -62(x + 1) = 9

Combine like terms: 1x + 1x = 2x
7(1 + 2x + x2) + -62(x + 1) = 9
(1 * 7 + 2x * 7 + x2 * 7) + -62(x + 1) = 9
(7 + 14x + 7x2) + -62(x + 1) = 9

Reorder the terms:
7 + 14x + 7x2 + -62(1 + x) = 9
7 + 14x + 7x2 + (1 * -62 + x * -62) = 9
7 + 14x + 7x2 + (-62 + -62x) = 9

Reorder the terms:
7 + -62 + 14x + -62x + 7x2 = 9

Combine like terms: 7 + -62 = -55
-55 + 14x + -62x + 7x2 = 9

Combine like terms: 14x + -62x = -48x
-55 + -48x + 7x2 = 9

Solving
-55 + -48x + 7x2 = 9

Solving for variable 'x'.

Reorder the terms:
-55 + -9 + -48x + 7x2 = 9 + -9

Combine like terms: -55 + -9 = -64
-64 + -48x + 7x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-64 + -48x + 7x2 = 0

Factor a trinomial.
(-8 + -7x)(8 + -1x) = 0

Subproblem 1

Set the factor '(-8 + -7x)' equal to zero and attempt to solve: Simplifying -8 + -7x = 0 Solving -8 + -7x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + -7x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -7x = 0 + 8 -7x = 0 + 8 Combine like terms: 0 + 8 = 8 -7x = 8 Divide each side by '-7'. x = -1.142857143 Simplifying x = -1.142857143

Subproblem 2

Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8

Solution

x = {-1.142857143, 8}

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