(x+9)(x-7)=(2x+1)(x-7)

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Solution for (x+9)(x-7)=(2x+1)(x-7) equation:


Simplifying
(x + 9)(x + -7) = (2x + 1)(x + -7)

Reorder the terms:
(9 + x)(x + -7) = (2x + 1)(x + -7)

Reorder the terms:
(9 + x)(-7 + x) = (2x + 1)(x + -7)

Multiply (9 + x) * (-7 + x)
(9(-7 + x) + x(-7 + x)) = (2x + 1)(x + -7)
((-7 * 9 + x * 9) + x(-7 + x)) = (2x + 1)(x + -7)
((-63 + 9x) + x(-7 + x)) = (2x + 1)(x + -7)
(-63 + 9x + (-7 * x + x * x)) = (2x + 1)(x + -7)
(-63 + 9x + (-7x + x2)) = (2x + 1)(x + -7)

Combine like terms: 9x + -7x = 2x
(-63 + 2x + x2) = (2x + 1)(x + -7)

Reorder the terms:
-63 + 2x + x2 = (1 + 2x)(x + -7)

Reorder the terms:
-63 + 2x + x2 = (1 + 2x)(-7 + x)

Multiply (1 + 2x) * (-7 + x)
-63 + 2x + x2 = (1(-7 + x) + 2x * (-7 + x))
-63 + 2x + x2 = ((-7 * 1 + x * 1) + 2x * (-7 + x))
-63 + 2x + x2 = ((-7 + 1x) + 2x * (-7 + x))
-63 + 2x + x2 = (-7 + 1x + (-7 * 2x + x * 2x))
-63 + 2x + x2 = (-7 + 1x + (-14x + 2x2))

Combine like terms: 1x + -14x = -13x
-63 + 2x + x2 = (-7 + -13x + 2x2)

Solving
-63 + 2x + x2 = -7 + -13x + 2x2

Solving for variable 'x'.

Reorder the terms:
-63 + 7 + 2x + 13x + x2 + -2x2 = -7 + -13x + 2x2 + 7 + 13x + -2x2

Combine like terms: -63 + 7 = -56
-56 + 2x + 13x + x2 + -2x2 = -7 + -13x + 2x2 + 7 + 13x + -2x2

Combine like terms: 2x + 13x = 15x
-56 + 15x + x2 + -2x2 = -7 + -13x + 2x2 + 7 + 13x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-56 + 15x + -1x2 = -7 + -13x + 2x2 + 7 + 13x + -2x2

Reorder the terms:
-56 + 15x + -1x2 = -7 + 7 + -13x + 13x + 2x2 + -2x2

Combine like terms: -7 + 7 = 0
-56 + 15x + -1x2 = 0 + -13x + 13x + 2x2 + -2x2
-56 + 15x + -1x2 = -13x + 13x + 2x2 + -2x2

Combine like terms: -13x + 13x = 0
-56 + 15x + -1x2 = 0 + 2x2 + -2x2
-56 + 15x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-56 + 15x + -1x2 = 0

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

Subproblem 1

Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 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 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8

Subproblem 2

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

Solution

x = {8, 7}

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