4x^2-19x+24=4x+9

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Solution for 4x^2-19x+24=4x+9 equation:


Simplifying
4x2 + -19x + 24 = 4x + 9

Reorder the terms:
24 + -19x + 4x2 = 4x + 9

Reorder the terms:
24 + -19x + 4x2 = 9 + 4x

Solving
24 + -19x + 4x2 = 9 + 4x

Solving for variable 'x'.

Reorder the terms:
24 + -9 + -19x + -4x + 4x2 = 9 + 4x + -9 + -4x

Combine like terms: 24 + -9 = 15
15 + -19x + -4x + 4x2 = 9 + 4x + -9 + -4x

Combine like terms: -19x + -4x = -23x
15 + -23x + 4x2 = 9 + 4x + -9 + -4x

Reorder the terms:
15 + -23x + 4x2 = 9 + -9 + 4x + -4x

Combine like terms: 9 + -9 = 0
15 + -23x + 4x2 = 0 + 4x + -4x
15 + -23x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
15 + -23x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(5 + -1x) = 0

Subproblem 1

Set the factor '(3 + -4x)' equal to zero and attempt to solve: Simplifying 3 + -4x = 0 Solving 3 + -4x = 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 + -4x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4x = 0 + -3 -4x = 0 + -3 Combine like terms: 0 + -3 = -3 -4x = -3 Divide each side by '-4'. x = 0.75 Simplifying x = 0.75

Subproblem 2

Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5

Solution

x = {0.75, 5}

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