7x^2-47=x^2-6x-11

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Solution for 7x^2-47=x^2-6x-11 equation:


Simplifying
7x2 + -47 = x2 + -6x + -11

Reorder the terms:
-47 + 7x2 = x2 + -6x + -11

Reorder the terms:
-47 + 7x2 = -11 + -6x + x2

Solving
-47 + 7x2 = -11 + -6x + x2

Solving for variable 'x'.

Reorder the terms:
-47 + 11 + 6x + 7x2 + -1x2 = -11 + -6x + x2 + 11 + 6x + -1x2

Combine like terms: -47 + 11 = -36
-36 + 6x + 7x2 + -1x2 = -11 + -6x + x2 + 11 + 6x + -1x2

Combine like terms: 7x2 + -1x2 = 6x2
-36 + 6x + 6x2 = -11 + -6x + x2 + 11 + 6x + -1x2

Reorder the terms:
-36 + 6x + 6x2 = -11 + 11 + -6x + 6x + x2 + -1x2

Combine like terms: -11 + 11 = 0
-36 + 6x + 6x2 = 0 + -6x + 6x + x2 + -1x2
-36 + 6x + 6x2 = -6x + 6x + x2 + -1x2

Combine like terms: -6x + 6x = 0
-36 + 6x + 6x2 = 0 + x2 + -1x2
-36 + 6x + 6x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-36 + 6x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + x + x2) = 0

Factor a trinomial.
6((-3 + -1x)(2 + -1x)) = 0

Ignore the factor 6.

Subproblem 1

Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3

Subproblem 2

Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 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 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2

Solution

x = {-3, 2}

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