(2x-3)(4x+1)=4

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Solution for (2x-3)(4x+1)=4 equation:


Simplifying
(2x + -3)(4x + 1) = 4

Reorder the terms:
(-3 + 2x)(4x + 1) = 4

Reorder the terms:
(-3 + 2x)(1 + 4x) = 4

Multiply (-3 + 2x) * (1 + 4x)
(-3(1 + 4x) + 2x * (1 + 4x)) = 4
((1 * -3 + 4x * -3) + 2x * (1 + 4x)) = 4
((-3 + -12x) + 2x * (1 + 4x)) = 4
(-3 + -12x + (1 * 2x + 4x * 2x)) = 4
(-3 + -12x + (2x + 8x2)) = 4

Combine like terms: -12x + 2x = -10x
(-3 + -10x + 8x2) = 4

Solving
-3 + -10x + 8x2 = 4

Solving for variable 'x'.

Reorder the terms:
-3 + -4 + -10x + 8x2 = 4 + -4

Combine like terms: -3 + -4 = -7
-7 + -10x + 8x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-7 + -10x + 8x2 = 0

Factor a trinomial.
(-1 + -2x)(7 + -4x) = 0

Subproblem 1

Set the factor '(-1 + -2x)' equal to zero and attempt to solve: Simplifying -1 + -2x = 0 Solving -1 + -2x = 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 + -2x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2x = 0 + 1 -2x = 0 + 1 Combine like terms: 0 + 1 = 1 -2x = 1 Divide each side by '-2'. x = -0.5 Simplifying x = -0.5

Subproblem 2

Set the factor '(7 + -4x)' equal to zero and attempt to solve: Simplifying 7 + -4x = 0 Solving 7 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -4x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4x = 0 + -7 -4x = 0 + -7 Combine like terms: 0 + -7 = -7 -4x = -7 Divide each side by '-4'. x = 1.75 Simplifying x = 1.75

Solution

x = {-0.5, 1.75}

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