4x^2-19x+23=-3x+8

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Solution for 4x^2-19x+23=-3x+8 equation:


Simplifying
4x2 + -19x + 23 = -3x + 8

Reorder the terms:
23 + -19x + 4x2 = -3x + 8

Reorder the terms:
23 + -19x + 4x2 = 8 + -3x

Solving
23 + -19x + 4x2 = 8 + -3x

Solving for variable 'x'.

Reorder the terms:
23 + -8 + -19x + 3x + 4x2 = 8 + -3x + -8 + 3x

Combine like terms: 23 + -8 = 15
15 + -19x + 3x + 4x2 = 8 + -3x + -8 + 3x

Combine like terms: -19x + 3x = -16x
15 + -16x + 4x2 = 8 + -3x + -8 + 3x

Reorder the terms:
15 + -16x + 4x2 = 8 + -8 + -3x + 3x

Combine like terms: 8 + -8 = 0
15 + -16x + 4x2 = 0 + -3x + 3x
15 + -16x + 4x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
15 + -16x + 4x2 = 0

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

Subproblem 1

Set the factor '(3 + -2x)' equal to zero and attempt to solve: Simplifying 3 + -2x = 0 Solving 3 + -2x = 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 + -2x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2x = 0 + -3 -2x = 0 + -3 Combine like terms: 0 + -3 = -3 -2x = -3 Divide each side by '-2'. x = 1.5 Simplifying x = 1.5

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 = {1.5, 2.5}

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