(7x+1)(3x-4)-(5x-2)(x-4)+3x-13=0

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Solution for (7x+1)(3x-4)-(5x-2)(x-4)+3x-13=0 equation: 


Simplifying
(7x + 1)(3x + -4) + -1(5x + -2)(x + -4) + 3x + -13 = 0

Reorder the terms:
(1 + 7x)(3x + -4) + -1(5x + -2)(x + -4) + 3x + -13 = 0

Reorder the terms:
(1 + 7x)(-4 + 3x) + -1(5x + -2)(x + -4) + 3x + -13 = 0

Multiply (1 + 7x) * (-4 + 3x)
(1(-4 + 3x) + 7x * (-4 + 3x)) + -1(5x + -2)(x + -4) + 3x + -13 = 0
((-4 * 1 + 3x * 1) + 7x * (-4 + 3x)) + -1(5x + -2)(x + -4) + 3x + -13 = 0
((-4 + 3x) + 7x * (-4 + 3x)) + -1(5x + -2)(x + -4) + 3x + -13 = 0
(-4 + 3x + (-4 * 7x + 3x * 7x)) + -1(5x + -2)(x + -4) + 3x + -13 = 0
(-4 + 3x + (-28x + 21x2)) + -1(5x + -2)(x + -4) + 3x + -13 = 0

Combine like terms: 3x + -28x = -25x
(-4 + -25x + 21x2) + -1(5x + -2)(x + -4) + 3x + -13 = 0

Reorder the terms:
-4 + -25x + 21x2 + -1(-2 + 5x)(x + -4) + 3x + -13 = 0

Reorder the terms:
-4 + -25x + 21x2 + -1(-2 + 5x)(-4 + x) + 3x + -13 = 0

Multiply (-2 + 5x) * (-4 + x)
-4 + -25x + 21x2 + -1(-2(-4 + x) + 5x * (-4 + x)) + 3x + -13 = 0
-4 + -25x + 21x2 + -1((-4 * -2 + x * -2) + 5x * (-4 + x)) + 3x + -13 = 0
-4 + -25x + 21x2 + -1((8 + -2x) + 5x * (-4 + x)) + 3x + -13 = 0
-4 + -25x + 21x2 + -1(8 + -2x + (-4 * 5x + x * 5x)) + 3x + -13 = 0
-4 + -25x + 21x2 + -1(8 + -2x + (-20x + 5x2)) + 3x + -13 = 0

Combine like terms: -2x + -20x = -22x
-4 + -25x + 21x2 + -1(8 + -22x + 5x2) + 3x + -13 = 0
-4 + -25x + 21x2 + (8 * -1 + -22x * -1 + 5x2 * -1) + 3x + -13 = 0
-4 + -25x + 21x2 + (-8 + 22x + -5x2) + 3x + -13 = 0

Reorder the terms:
-4 + -8 + -13 + -25x + 22x + 3x + 21x2 + -5x2 = 0

Combine like terms: -4 + -8 = -12
-12 + -13 + -25x + 22x + 3x + 21x2 + -5x2 = 0

Combine like terms: -12 + -13 = -25
-25 + -25x + 22x + 3x + 21x2 + -5x2 = 0

Combine like terms: -25x + 22x = -3x
-25 + -3x + 3x + 21x2 + -5x2 = 0

Combine like terms: -3x + 3x = 0
-25 + 0 + 21x2 + -5x2 = 0
-25 + 21x2 + -5x2 = 0

Combine like terms: 21x2 + -5x2 = 16x2
-25 + 16x2 = 0

Solving
-25 + 16x2 = 0

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '25' to each side of the equation.
-25 + 25 + 16x2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 16x2 = 0 + 25
16x2 = 0 + 25

Combine like terms: 0 + 25 = 25
16x2 = 25

Divide each side by '16'.
x2 = 1.5625

Simplifying
x2 = 1.5625

Take the square root of each side:
x = {-1.25, 1.25}

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