(2x+1)(x-7)+(x-3)(x-7)=0

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Solution for (2x+1)(x-7)+(x-3)(x-7)=0 equation:


Simplifying
(2x + 1)(x + -7) + (x + -3)(x + -7) = 0

Reorder the terms:
(1 + 2x)(x + -7) + (x + -3)(x + -7) = 0

Reorder the terms:
(1 + 2x)(-7 + x) + (x + -3)(x + -7) = 0

Multiply (1 + 2x) * (-7 + x)
(1(-7 + x) + 2x * (-7 + x)) + (x + -3)(x + -7) = 0
((-7 * 1 + x * 1) + 2x * (-7 + x)) + (x + -3)(x + -7) = 0
((-7 + 1x) + 2x * (-7 + x)) + (x + -3)(x + -7) = 0
(-7 + 1x + (-7 * 2x + x * 2x)) + (x + -3)(x + -7) = 0
(-7 + 1x + (-14x + 2x2)) + (x + -3)(x + -7) = 0

Combine like terms: 1x + -14x = -13x
(-7 + -13x + 2x2) + (x + -3)(x + -7) = 0

Reorder the terms:
-7 + -13x + 2x2 + (-3 + x)(x + -7) = 0

Reorder the terms:
-7 + -13x + 2x2 + (-3 + x)(-7 + x) = 0

Multiply (-3 + x) * (-7 + x)
-7 + -13x + 2x2 + (-3(-7 + x) + x(-7 + x)) = 0
-7 + -13x + 2x2 + ((-7 * -3 + x * -3) + x(-7 + x)) = 0
-7 + -13x + 2x2 + ((21 + -3x) + x(-7 + x)) = 0
-7 + -13x + 2x2 + (21 + -3x + (-7 * x + x * x)) = 0
-7 + -13x + 2x2 + (21 + -3x + (-7x + x2)) = 0

Combine like terms: -3x + -7x = -10x
-7 + -13x + 2x2 + (21 + -10x + x2) = 0

Reorder the terms:
-7 + 21 + -13x + -10x + 2x2 + x2 = 0

Combine like terms: -7 + 21 = 14
14 + -13x + -10x + 2x2 + x2 = 0

Combine like terms: -13x + -10x = -23x
14 + -23x + 2x2 + x2 = 0

Combine like terms: 2x2 + x2 = 3x2
14 + -23x + 3x2 = 0

Solving
14 + -23x + 3x2 = 0

Solving for variable 'x'.

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

Subproblem 1

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

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 = {0.6666666667, 7}

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