4x^2+2x-6=24

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Solution for 4x^2+2x-6=24 equation:


Simplifying
4x2 + 2x + -6 = 24

Reorder the terms:
-6 + 2x + 4x2 = 24

Solving
-6 + 2x + 4x2 = 24

Solving for variable 'x'.

Reorder the terms:
-6 + -24 + 2x + 4x2 = 24 + -24

Combine like terms: -6 + -24 = -30
-30 + 2x + 4x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-30 + 2x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + x + 2x2) = 0

Factor a trinomial.
2((-3 + -1x)(5 + -2x)) = 0

Ignore the factor 2.

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 '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5

Solution

x = {-3, 2.5}

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