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

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


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

Multiply (5 + -3x) * (3 + 4x)
(5(3 + 4x) + -3x * (3 + 4x)) + -1(7 + 3x)(1 + -4x) + 1 = 0
((3 * 5 + 4x * 5) + -3x * (3 + 4x)) + -1(7 + 3x)(1 + -4x) + 1 = 0
((15 + 20x) + -3x * (3 + 4x)) + -1(7 + 3x)(1 + -4x) + 1 = 0
(15 + 20x + (3 * -3x + 4x * -3x)) + -1(7 + 3x)(1 + -4x) + 1 = 0
(15 + 20x + (-9x + -12x2)) + -1(7 + 3x)(1 + -4x) + 1 = 0

Combine like terms: 20x + -9x = 11x
(15 + 11x + -12x2) + -1(7 + 3x)(1 + -4x) + 1 = 0

Multiply (7 + 3x) * (1 + -4x)
15 + 11x + -12x2 + -1(7(1 + -4x) + 3x * (1 + -4x)) + 1 = 0
15 + 11x + -12x2 + -1((1 * 7 + -4x * 7) + 3x * (1 + -4x)) + 1 = 0
15 + 11x + -12x2 + -1((7 + -28x) + 3x * (1 + -4x)) + 1 = 0
15 + 11x + -12x2 + -1(7 + -28x + (1 * 3x + -4x * 3x)) + 1 = 0
15 + 11x + -12x2 + -1(7 + -28x + (3x + -12x2)) + 1 = 0

Combine like terms: -28x + 3x = -25x
15 + 11x + -12x2 + -1(7 + -25x + -12x2) + 1 = 0
15 + 11x + -12x2 + (7 * -1 + -25x * -1 + -12x2 * -1) + 1 = 0
15 + 11x + -12x2 + (-7 + 25x + 12x2) + 1 = 0

Reorder the terms:
15 + -7 + 1 + 11x + 25x + -12x2 + 12x2 = 0

Combine like terms: 15 + -7 = 8
8 + 1 + 11x + 25x + -12x2 + 12x2 = 0

Combine like terms: 8 + 1 = 9
9 + 11x + 25x + -12x2 + 12x2 = 0

Combine like terms: 11x + 25x = 36x
9 + 36x + -12x2 + 12x2 = 0

Combine like terms: -12x2 + 12x2 = 0
9 + 36x + 0 = 0
9 + 36x = 0

Solving
9 + 36x = 0

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + -9 + 36x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 36x = 0 + -9
36x = 0 + -9

Combine like terms: 0 + -9 = -9
36x = -9

Divide each side by '36'.
x = -0.25

Simplifying
x = -0.25

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