5x+6=4x^2-24x+36

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Solution for 5x+6=4x^2-24x+36 equation:


Simplifying
5x + 6 = 4x2 + -24x + 36

Reorder the terms:
6 + 5x = 4x2 + -24x + 36

Reorder the terms:
6 + 5x = 36 + -24x + 4x2

Solving
6 + 5x = 36 + -24x + 4x2

Solving for variable 'x'.

Reorder the terms:
6 + -36 + 5x + 24x + -4x2 = 36 + -24x + 4x2 + -36 + 24x + -4x2

Combine like terms: 6 + -36 = -30
-30 + 5x + 24x + -4x2 = 36 + -24x + 4x2 + -36 + 24x + -4x2

Combine like terms: 5x + 24x = 29x
-30 + 29x + -4x2 = 36 + -24x + 4x2 + -36 + 24x + -4x2

Reorder the terms:
-30 + 29x + -4x2 = 36 + -36 + -24x + 24x + 4x2 + -4x2

Combine like terms: 36 + -36 = 0
-30 + 29x + -4x2 = 0 + -24x + 24x + 4x2 + -4x2
-30 + 29x + -4x2 = -24x + 24x + 4x2 + -4x2

Combine like terms: -24x + 24x = 0
-30 + 29x + -4x2 = 0 + 4x2 + -4x2
-30 + 29x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
-30 + 29x + -4x2 = 0

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

Subproblem 1

Set the factor '(-6 + x)' equal to zero and attempt to solve: Simplifying -6 + x = 0 Solving -6 + x = 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 + x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + x = 0 + 6 x = 0 + 6 Combine like terms: 0 + 6 = 6 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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