4x^2+12x-6=24-7x

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Solution for 4x^2+12x-6=24-7x equation:


Simplifying
4x2 + 12x + -6 = 24 + -7x

Reorder the terms:
-6 + 12x + 4x2 = 24 + -7x

Solving
-6 + 12x + 4x2 = 24 + -7x

Solving for variable 'x'.

Reorder the terms:
-6 + -24 + 12x + 7x + 4x2 = 24 + -7x + -24 + 7x

Combine like terms: -6 + -24 = -30
-30 + 12x + 7x + 4x2 = 24 + -7x + -24 + 7x

Combine like terms: 12x + 7x = 19x
-30 + 19x + 4x2 = 24 + -7x + -24 + 7x

Reorder the terms:
-30 + 19x + 4x2 = 24 + -24 + -7x + 7x

Combine like terms: 24 + -24 = 0
-30 + 19x + 4x2 = 0 + -7x + 7x
-30 + 19x + 4x2 = -7x + 7x

Combine like terms: -7x + 7x = 0
-30 + 19x + 4x2 = 0

Factor a trinomial.
(-6 + -1x)(5 + -4x) = 0

Subproblem 1

Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6

Subproblem 2

Set the factor '(5 + -4x)' equal to zero and attempt to solve: Simplifying 5 + -4x = 0 Solving 5 + -4x = 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 + -4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -4x = 0 + -5 -4x = 0 + -5 Combine like terms: 0 + -5 = -5 -4x = -5 Divide each side by '-4'. x = 1.25 Simplifying x = 1.25

Solution

x = {-6, 1.25}

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