4x^2-3x+6=4x+3

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Solution for 4x^2-3x+6=4x+3 equation:


Simplifying
4x2 + -3x + 6 = 4x + 3

Reorder the terms:
6 + -3x + 4x2 = 4x + 3

Reorder the terms:
6 + -3x + 4x2 = 3 + 4x

Solving
6 + -3x + 4x2 = 3 + 4x

Solving for variable 'x'.

Reorder the terms:
6 + -3 + -3x + -4x + 4x2 = 3 + 4x + -3 + -4x

Combine like terms: 6 + -3 = 3
3 + -3x + -4x + 4x2 = 3 + 4x + -3 + -4x

Combine like terms: -3x + -4x = -7x
3 + -7x + 4x2 = 3 + 4x + -3 + -4x

Reorder the terms:
3 + -7x + 4x2 = 3 + -3 + 4x + -4x

Combine like terms: 3 + -3 = 0
3 + -7x + 4x2 = 0 + 4x + -4x
3 + -7x + 4x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
3 + -7x + 4x2 = 0

Factor a trinomial.
(3 + -4x)(1 + -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 '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Solution

x = {0.75, 1}

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