7x^2-14x-23=6x^2-23x+29

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Solution for 7x^2-14x-23=6x^2-23x+29 equation:


Simplifying
7x2 + -14x + -23 = 6x2 + -23x + 29

Reorder the terms:
-23 + -14x + 7x2 = 6x2 + -23x + 29

Reorder the terms:
-23 + -14x + 7x2 = 29 + -23x + 6x2

Solving
-23 + -14x + 7x2 = 29 + -23x + 6x2

Solving for variable 'x'.

Reorder the terms:
-23 + -29 + -14x + 23x + 7x2 + -6x2 = 29 + -23x + 6x2 + -29 + 23x + -6x2

Combine like terms: -23 + -29 = -52
-52 + -14x + 23x + 7x2 + -6x2 = 29 + -23x + 6x2 + -29 + 23x + -6x2

Combine like terms: -14x + 23x = 9x
-52 + 9x + 7x2 + -6x2 = 29 + -23x + 6x2 + -29 + 23x + -6x2

Combine like terms: 7x2 + -6x2 = 1x2
-52 + 9x + 1x2 = 29 + -23x + 6x2 + -29 + 23x + -6x2

Reorder the terms:
-52 + 9x + 1x2 = 29 + -29 + -23x + 23x + 6x2 + -6x2

Combine like terms: 29 + -29 = 0
-52 + 9x + 1x2 = 0 + -23x + 23x + 6x2 + -6x2
-52 + 9x + 1x2 = -23x + 23x + 6x2 + -6x2

Combine like terms: -23x + 23x = 0
-52 + 9x + 1x2 = 0 + 6x2 + -6x2
-52 + 9x + 1x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-52 + 9x + 1x2 = 0

Factor a trinomial.
(-13 + -1x)(4 + -1x) = 0

Subproblem 1

Set the factor '(-13 + -1x)' equal to zero and attempt to solve: Simplifying -13 + -1x = 0 Solving -13 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -1x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -1x = 0 + 13 -1x = 0 + 13 Combine like terms: 0 + 13 = 13 -1x = 13 Divide each side by '-1'. x = -13 Simplifying x = -13

Subproblem 2

Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4

Solution

x = {-13, 4}

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